From d77addeaf8c147f221dada83270725920669e0c0 Mon Sep 17 00:00:00 2001 From: jgarnek Date: Fri, 23 Dec 2022 12:52:17 +0000 Subject: [PATCH] praca nad as_cech coordinate; przed poprawa drugiej czesci --- sage/.run.term-0.term | 11662 +++++++++++++++++++++++- sage/as_covers/as_cech_class.sage | 40 +- sage/as_covers/as_cover_class.sage | 55 +- sage/as_covers/as_form_class.sage | 22 +- sage/as_covers/as_function_class.sage | 6 +- 5 files changed, 11731 insertions(+), 54 deletions(-) diff --git a/sage/.run.term-0.term b/sage/.run.term-0.term index 8d9e944..a5d06eb 100644 --- a/sage/.run.term-0.term +++ b/sage/.run.term-0.term @@ -1032,4 +1032,11664 @@ Untracked files: superelliptic_arbitrary_field.ipynb no changes added to commit (use "git add" and/or "git commit -a") -]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add sage/as_ \ No newline at end of file +]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add sage/as_covers/as_reduction.sage +]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add -u +]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git commit -m ""a"s" "r"e"d"u"c"t"i"o"n" "("s"r"a"""t"a"r"e")" "p"l"u"s" "m"a"c"i"e"r"z" "d"z"i"a"l"a"n"i"a" "n"a" "b"a"z"i"e" "d"R" "p"r"a"w"i"e" "d"z"i"a"l"a" +[master 6494187] as reduction (stare) plus macierz dzialania na bazie dR prawie dziala + 9 files changed, 1155 insertions(+), 14959 deletions(-) + rewrite sage/.run.term-0.term (97%) + create mode 100644 sage/as_covers/as_reduction.sage +]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$ git commit -m "as reduction (stare) plus macierz dzialania na bazie dR prawie dziala" add -ucommit -m "as reduction (stare) plus macierz dzialania na bazie dR prawie dziala" sage +┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.7, Release Date: 2022-09-19 │ +│ Using Python 3.10.5. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +(1) * dx +(1) * dx +(z1) * dx +(z1) * dx +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx +(z0 + 1) * dx +(z0 + 1) * dx +(z0*z1 + z1) * dx +(z0*z1 + z1) * dx +(z0^2 - z0 + 1) * dx +(z0^2 - z0 + 1) * dx +(x) * dx +(x) * dx +(-x*z0^2 + x*z0 + x*z1 - x) * dx +(-x*z0^2 + x*z0 + x*z1 - x) * dx +(x*z0 + x) * dx +(x*z0 + x) * dx +(x^2) * dx +(x^2) * dx +(0) * dx +(0) * dx +(0) * dx +(0) * dx +(x^2) * dx +(x^2) * dx +(x^2 - z0*z1 + z1) * dx +(x^2 - z0*z1 + z1) * dx +(x^2) * dx +(x^2) * dx +(x^2*z0 + z0^2*z1 + z1^2) * dx +(x^2*z0 + z0^2*z1 + z1^2) * dx +(x*z0 - x) * dx +(x*z0 - x) * dx +(x*z0^2 - x*z1) * dx +(x*z0^2 - x*z1) * dx +(x*z0^2 - x*z0 - x*z1 + x) * dx +(x*z0^2 - x*z0 - x*z1 + x) * dx +((x^4 - x^2*z0*z1 + x^2*z1 + z1^2 + z1)/x^2) * dx +((x^4 - x^2*z0*z1 + x^2*z1 + z1^2 + z1)/x^2) * dx +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [1], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :71, in coordinates(self, threshold, basis) + +File :84, in coordinates(self, basis) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_() + 786 return self._call_with_args(x, args, kwds) + 787 +--> 788 cpdef Element _call_(self, x): + 789 """ + 790 Call method with a single argument, not implemented in the base class. + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check) + 1249 return num + 1250 if check and not den.is_unit(): + 1251 # This should probably be a ValueError. + 1252 # However, too much existing code is expecting this to throw a + 1253 # TypeError, so we decided to keep it for the time being. +-> 1254 raise TypeError("fraction must have unit denominator") + 1255 return num * den.inverse_of_unit() + +TypeError: fraction must have unit denominator +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?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)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +[?2004h[?25l[?7lsage: [?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[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis() +[?7h[?12l[?25h[?2004l[?7h[(1) * dx, + (z1) * dx, + (x^2*z0 + z0^2*z1 + z1^2) * dx, + (z0) * dx, + (z0*z1) * dx, + (z0^2) * dx, + (x) * dx, + (-x*z0^2 + x*z1) * dx, + (x*z0) * dx, + (x^2) * dx] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage +┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.7, Release Date: 2022-09-19 │ +│ Using Python 3.10.5. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004lWARNING: your terminal doesn't support cursor position requests (CPR). +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +(1) * dx +(1) * dx +(z1) * dx +(z1) * dx +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx +(z0 + 1) * dx +(z0 + 1) * dx +(z0*z1 + z1) * dx +(z0*z1 + z1) * dx +(z0^2 - z0 + 1) * dx +(z0^2 - z0 + 1) * dx +(x) * dx +(x) * dx +(-x*z0^2 + x*z0 + x*z1 - x) * dx +(-x*z0^2 + x*z0 + x*z1 - x) * dx +(x*z0 + x) * dx +(x*z0 + x) * dx +(x^2) * dx +(x^2) * dx +(0) * dx +(0) * dx +(0) * dx +(0) * dx +(x^2) * dx +(x^2) * dx +(x^2 - z0*z1 + z1) * dx +(x^2 - z0*z1 + z1) * dx +(x^2) * dx +(x^2) * dx +(x^2*z0 + z0^2*z1 + z1^2) * dx +(x^2*z0 + z0^2*z1 + z1^2) * dx +(x*z0 - x) * dx +(x*z0 - x) * dx +(x*z0^2 - x*z1) * dx +(x*z0^2 - x*z1) * dx +(x*z0^2 - x*z0 - x*z1 + x) * dx +(x*z0^2 - x*z0 - x*z1 + x) * dx +((x^4 - x^2*z0*z1 + x^2*z1 + z1^2 + z1)/x^2) * dx +((x^4 - x^2*z0*z1 + x^2*z1 + z1^2 + z1)/x^2) * dx +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [1], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :71, in coordinates(self, threshold, basis) + +File :84, in coordinates(self, basis) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_() + 786 return self._call_with_args(x, args, kwds) + 787 +--> 788 cpdef Element _call_(self, x): + 789 """ + 790 Call method with a single argument, not implemented in the base class. + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check) + 1249 return num + 1250 if check and not den.is_unit(): + 1251 # This should probably be a ValueError. + 1252 # However, too much existing code is expecting this to throw a + 1253 # TypeError, so we decided to keep it for the time being. +-> 1254 raise TypeError("fraction must have unit denominator") + 1255 return num * den.inverse_of_unit() + +TypeError: fraction must have unit denominator +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A, B, text=True)[?7h[?12l[?25h[?25l[?7l()l[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lT[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +(1) * dx +(1) * dx +(z1) * dx +(z1) * dx +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx +(z0 + 1) * dx +(z0 + 1) * dx +(z0*z1 + z1) * dx +(z0*z1 + z1) * dx +(z0^2 - z0 + 1) * dx +(z0^2 - z0 + 1) * dx +(x) * dx +(x) * dx +(-x*z0^2 + x*z0 + x*z1 - x) * dx +(-x*z0^2 + x*z0 + x*z1 - x) * dx +(x*z0 + x) * dx +(x*z0 + x) * dx +(x^2) * dx +(x^2) * dx +(0) * dx +(0) * dx +(0) * dx +(0) * dx +(x^2) * dx +(x^2) * dx +(x^2 - z0*z1 + z1) * dx +(x^2 - z0*z1 + z1) * dx +(x^2) * dx +(x^2) * dx +(x^2*z0 + z0^2*z1 + z1^2) * dx +(x^2*z0 + z0^2*z1 + z1^2) * dx +(x*z0 - x) * dx +(x*z0 - x) * dx +(x*z0^2 - x*z1) * dx +(x*z0^2 - x*z1) * dx +(x*z0^2 - x*z0 - x*z1 + x) * dx +(x*z0^2 - x*z0 - x*z1 + x) * dx +((x^4 - x^2*z0*z1 + x^2*z1 + z1^2 + z1)/x^2) * dx +((x^4 - x^2*z0*z1 + x^2*z1 + z1^2 + z1)/x^2) * dx +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [2], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :71, in coordinates(self, threshold, basis) + +File :84, in coordinates(self, basis) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_() + 786 return self._call_with_args(x, args, kwds) + 787 +--> 788 cpdef Element _call_(self, x): + 789 """ + 790 Call method with a single argument, not implemented in the base class. + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check) + 1249 return num + 1250 if check and not den.is_unit(): + 1251 # This should probably be a ValueError. + 1252 # However, too much existing code is expecting this to throw a + 1253 # TypeError, so we decided to keep it for the time being. +-> 1254 raise TypeError("fraction must have unit denominator") + 1255 return num * den.inverse_of_unit() + +TypeError: fraction must have unit denominator +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: AS.x +[?7h[?12l[?25h[?2004l[?7hx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.x[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: AS.y +[?7h[?12l[?25h[?2004l[?7hy +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.y[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7lsage: AS.z +[?7h[?12l[?25h[?2004l[?7h[z0, z1] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.z[?7h[?12l[?25h[?25l[?7lS[?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[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +(1) * dx +(1) * dx +(z1) * dx +(z1) * dx +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx +(z0 + 1) * dx +(z0 + 1) * dx +(z0*z1 + z1) * dx +(z0*z1 + z1) * dx +(z0^2 - z0 + 1) * dx +(z0^2 - z0 + 1) * dx +(x) * dx +(x) * dx +(-x*z0^2 + x*z0 + x*z1 - x) * dx +(-x*z0^2 + x*z0 + x*z1 - x) * dx +(x*z0 + x) * dx +(x*z0 + x) * dx +(x^2) * dx +(x^2) * dx +(0) * dx +(0) * dx +(0) * dx +(0) * dx +(x^2) * dx +(x^2) * dx +(x^2 - z0*z1 + z1) * dx +(x^2 - z0*z1 + z1) * dx +(x^2) * dx +(x^2) * dx +(x^2*z0 + z0^2*z1 + z1^2) * dx +(x^2*z0 + z0^2*z1 + z1^2) * dx +(x*z0 - x) * dx +(x*z0 - x) * dx +(x*z0^2 - x*z1) * dx +(x*z0^2 - x*z1) * dx +(x*z0^2 - x*z0 - x*z1 + x) * dx +(x*z0^2 - x*z0 - x*z1 + x) * dx +((x^4 - x^2*z0*z1 + x^2*z1 + z1^2 + z1)/x^2) * dx +((x^4 - x^2*z0*z1 + x^2*z1 + z1^2 + z1)/x^2) * dx +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [6], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :71, in coordinates(self, threshold, basis) + +File :84, in coordinates(self, basis) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_() + 786 return self._call_with_args(x, args, kwds) + 787 +--> 788 cpdef Element _call_(self, x): + 789 """ + 790 Call method with a single argument, not implemented in the base class. + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check) + 1249 return num + 1250 if check and not den.is_unit(): + 1251 # This should probably be a ValueError. + 1252 # However, too much existing code is expecting this to throw a + 1253 # TypeError, so we decided to keep it for the time being. +-> 1254 raise TypeError("fraction must have unit denominator") + 1255 return num * den.inverse_of_unit() + +TypeError: fraction must have unit denominator +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lzmag = AS.magical_element(threshold = 18)[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[?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[?7lAS.z[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[1][?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lX[?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.x[?7h[?12l[?25h[?25l[?7lS.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: AS.z[1]^2/AS.x*AS.dx +[?7h[?12l[?25h[?2004l[?7h(z1^2/x) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.z[1]^2/AS.x*AS.dx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[1]^2/AS.x*AS.dx)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?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[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (AS.z[1]^2/AS.x*AS.dx).valuation() +[?7h[?12l[?25h[?2004l[?7h3 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[1]^2/AS.x*AS.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[?7lAS.z[1]^2/AS.x*AS.dx[?7h[?12l[?25h[?25l[?7l(AS.z[1]^2/AS.x*AS.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[?7lr[?7h[?12l[?25h[?25l[?7lu[?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[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l('init.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +0 +(1) * dx +(1) * dx +0 +(z1) * dx +(z1) * dx +0 +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx +0 +(z0 + 1) * dx +(z0 + 1) * dx +0 +(z0*z1 + z1) * dx +(z0*z1 + z1) * dx +0 +(z0^2 - z0 + 1) * dx +(z0^2 - z0 + 1) * dx +0 +(x) * dx +(x) * dx +0 +(-x*z0^2 + x*z0 + x*z1 - x) * dx +(-x*z0^2 + x*z0 + x*z1 - x) * dx +0 +(x*z0 + x) * dx +(x*z0 + x) * dx +0 +(x^2) * dx +(x^2) * dx +0 +(0) * dx +(0) * dx +0 +(0) * dx +(0) * dx +0 +(x^2) * dx +(x^2) * dx +0 +(x^2 - z0*z1 + z1) * dx +(x^2 - z0*z1 + z1) * dx +0 +(x^2) * dx +(x^2) * dx +0 +(x^2*z0 + z0^2*z1 + z1^2) * dx +(x^2*z0 + z0^2*z1 + z1^2) * dx +0 +(x*z0 - x) * dx +(x*z0 - x) * dx +0 +(x*z0^2 - x*z1) * dx +(x*z0^2 - x*z1) * dx +0 +(x*z0^2 - x*z0 - x*z1 + x) * dx +(x*z0^2 - x*z0 - x*z1 + x) * dx +(x^2*z1 - z0*z1^2 + z1^2)/x^3 +((x^4 - x^2*z0*z1 + x^2*z1 + z1^2 + z1)/x^2) * dx +((x^4 - x^2*z0*z1 + x^2*z1 + z1^2 + z1)/x^2) * dx +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [9], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :71, in coordinates(self, threshold, basis) + +File :84, in coordinates(self, basis) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_() + 786 return self._call_with_args(x, args, kwds) + 787 +--> 788 cpdef Element _call_(self, x): + 789 """ + 790 Call method with a single argument, not implemented in the base class. + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check) + 1249 return num + 1250 if check and not den.is_unit(): + 1251 # This should probably be a ValueError. + 1252 # However, too much existing code is expecting this to throw a + 1253 # TypeError, so we decided to keep it for the time being. +-> 1254 raise TypeError("fraction must have unit denominator") + 1255 return num * den.inverse_of_unit() + +TypeError: fraction must have unit denominator +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(AS.z[1]^2/AS.x*AS.dx).valuation()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +0 +--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Input In [10], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :68, in coordinates(self, threshold, basis) + +File /ext/sage/9.7/src/sage/misc/functional.py:1388, in numerator(x) + 1386 if isinstance(x, int): + 1387 return x +-> 1388 return x.numerator() + +AttributeError: 'as_function' object has no attribute 'numerator' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +(x^2*z1 - z0*z1^2 + z1^2)/x^3 +(x^2*z1 - z0*z1^2)/x^3 +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [11], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :77, in coordinates(self, threshold, basis) + +File :84, in coordinates(self, basis) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_() + 786 return self._call_with_args(x, args, kwds) + 787 +--> 788 cpdef Element _call_(self, x): + 789 """ + 790 Call method with a single argument, not implemented in the base class. + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check) + 1249 return num + 1250 if check and not den.is_unit(): + 1251 # This should probably be a ValueError. + 1252 # However, too much existing code is expecting this to throw a + 1253 # TypeError, so we decided to keep it for the time being. +-> 1254 raise TypeError("fraction must have unit denominator") + 1255 return num * den.inverse_of_unit() + +TypeError: fraction must have unit denominator +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^2*z1 - z0*z1^2)/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[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lAx^2*z1 - z0*z1^2)/x^3[?7h[?12l[?25h[?25l[?7lSx^2*z1 - z0*z1^2)/x^3[?7h[?12l[?25h[?25l[?7l.x^2*z1 - z0*z1^2)/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[?7lAz1 - z0*z1^2)/x^3[?7h[?12l[?25h[?25l[?7lSz1 - z0*z1^2)/x^3[?7h[?12l[?25h[?25l[?7l.z1 - z0*z1^2)/x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1 - z0*z1^2)/x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[] - z0*z1^2)/x^3[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAz0*z1^2)/x^3[?7h[?12l[?25h[?25l[?7lSz0*z1^2)/x^3[?7h[?12l[?25h[?25l[?7l.z0*z1^2)/x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[0*z1^2)/x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]*z1^2)/x^3[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lAz1^2)/x^3[?7h[?12l[?25h[?25l[?7lSz1^2)/x^3[?7h[?12l[?25h[?25l[?7l.z1^2)/x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1^2)/x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]^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[?7lAx^3[?7h[?12l[?25h[?25l[?7lSx^3[?7h[?12l[?25h[?25l[?7l.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)^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(AS.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[?7lsage: (AS.x^2*AS.z[1] - AS.z[0]*AS.z[1]^2)/(AS.x)^3 +[?7h[?12l[?25h[?2004l[?7h(x^2*z1 - z0*z1^2)/x^3 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.x^2*AS.z[1] - AS.z[0]*AS.z[1]^2)/(AS.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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((AS.x^2*AS.z[1] - AS.z[0]*AS.z[1]^2)/(AS.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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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: ((AS.x^2*AS.z[1] - AS.z[0]*AS.z[1]^2)/(AS.x)^3).valuation() +[?7h[?12l[?25h[?2004l[?7h1 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR. = QQ[][?7h[?12l[?25h[?25l[?7lxy[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: Rxy +[?7h[?12l[?25h[?2004l[?7hMultivariate Polynomial Ring in x, y over Finite Field of size 3 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l = Rxy(x^2 + y^3)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lRxy(x^2 + y^3)[?7h[?12l[?25h[?25l[?7lsage: f = Rxy(x^2 + y^3) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = AS.genus()[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7lx6[?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[?7lx[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g = Rxy(x^5 + x*y) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = Rxy(x^5 + x*y)[?7h[?12l[?25h[?25l[?7l.parent()[?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: g.quo_rem(f) +[?7h[?12l[?25h[?2004l[?7h(0, x^5 + x*y) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx^2*z1 - z0*z1^2[?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[1 - z0*z1^2[?7h[?12l[?25h[?25l[?7l[] - z0*z1^2[?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[0*z1^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]*z1^2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]^2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: x^2*z[1] - z[0]*z[1]^2 +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Input In [18], in () +----> 1 x**Integer(2)*z[Integer(1)] - z[Integer(0)]*z[Integer(1)]**Integer(2) + +NameError: name 'z' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRxy[?7h[?12l[?25h[?25l[?7l. = QQ[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxy[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lzQ, Rxyz, x, y, z = AS.fct_field[?7h[?12l[?25h[?25l[?7l.<>[?7h[?12l[?25h[?25l[?7lx>[?7h[?12l[?25h[?25l[?7l,>[?7h[?12l[?25h[?25l[?7l >[?7h[?12l[?25h[?25l[?7ly>[?7h[?12l[?25h[?25l[?7l,>[?7h[?12l[?25h[?25l[?7l >[?7h[?12l[?25h[?25l[?7lz>[?7h[?12l[?25h[?25l[?7l0>[?7h[?12l[?25h[?25l[?7l,>[?7h[?12l[?25h[?25l[?7l >[?7h[?12l[?25h[?25l[?7lz>[?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[?7lP[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lG[?7h[?12l[?25h[?25l[?7lF[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l3[?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: Rxyz. = PolynomialRing(GF(3), 4) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx^2*z[1] - z[0]*z[1]^2[?7h[?12l[?25h[?25l[?7l, y = Rxyz.gens()[:2][?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l.g[?7h[?12l[?25h[?25l[?7lens[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: x, y, z0, z1 = Rxyz.gens() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx, y, z0, z1 = Rxyz.gens()[?7h[?12l[?25h[?25l[?7lRxyz. = PolynomialRing(GF(3), 4)[?7h[?12l[?25h[?25l[?7lx^2*z[1]- z[0]*[1]^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[^2[?7h[?12l[?25h[?25l[?7l^2[?7h[?12l[?25h[?25l[?7l^2[?7h[?12l[?25h[?25l[?7l1^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[*z1^2[?7h[?12l[?25h[?25l[?7l*z1^2[?7h[?12l[?25h[?25l[?7l*z1^2[?7h[?12l[?25h[?25l[?7l0*z1^2[?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[ - z0*z1^2[?7h[?12l[?25h[?25l[?7l - z0*z1^2[?7h[?12l[?25h[?25l[?7l - z0*z1^2[?7h[?12l[?25h[?25l[?7l1 - z0*z1^2[?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(x^2*z1 - z0*z1^2[?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[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (x^2*z1 - z0*z1^2).quo_rem(x^2) +[?7h[?12l[?25h[?2004l[?7h(z1, -z0*z1^2) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^2*z1 - z0*z1^2).quo_rem(x^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[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +(x^2*z1 - z0*z1^2 + z1^2)/x^3 +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [22], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :75, in coordinates(self, threshold, basis) + +File :84, in coordinates(self, basis) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_() + 786 return self._call_with_args(x, args, kwds) + 787 +--> 788 cpdef Element _call_(self, x): + 789 """ + 790 Call method with a single argument, not implemented in the base class. + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check) + 1249 return num + 1250 if check and not den.is_unit(): + 1251 # This should probably be a ValueError. + 1252 # However, too much existing code is expecting this to throw a + 1253 # TypeError, so we decided to keep it for the time being. +-> 1254 raise TypeError("fraction must have unit denominator") + 1255 return num * den.inverse_of_unit() + +TypeError: fraction must have unit denominator +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^2*z1 - z0*z1^2 + z1^2)/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[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((x^2*z1 - z0*z1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lAx^2*z1 - z0*z1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7lSx^2*z1 - z0*z1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7l.x^2*z1 - z0*z1^2 + z1^2)/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[?7lAz1 - z0*z1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7lSz1 - z0*z1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7l.z1 - z0*z1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1 - z0*z1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7lp1 - z0*z1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7l1 - z0*z1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[] - z0*z1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAz0*z1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7lSz0*z1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7l.z0*z1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[0*z1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]*z1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAz1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7lSz1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7l.z1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1^2 + z1^2)/x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]^2 + z1^2)/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[?7l[?7h[?12l[?25h[?25l[?7lAz1^2)/x^3[?7h[?12l[?25h[?25l[?7lSz1^2)/x^3[?7h[?12l[?25h[?25l[?7l.z1^2)/x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1^2)/x^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]^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[?7lAx^3[?7h[?12l[?25h[?25l[?7lSx^3[?7h[?12l[?25h[?25l[?7l.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[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ((AS.x^2*AS.z[1] - AS.z[0]*AS.z[1]^2 + AS.z[1]^2)/AS.x^3).valuation() +[?7h[?12l[?25h[?2004l[?7h1 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((AS.x^2*AS.z[1] - AS.z[0]*AS.z[1]^2 + AS.z[1]^2)/AS.x^3).valuation()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +0 +0 0 +0 +0 0 +0 +0 0 +0 +0 0 +0 +0 0 +0 +0 0 +0 +0 0 +0 +0 0 +0 +0 0 +0 +0 0 +0 +0 0 +0 +0 0 +0 +0 0 +0 +0 0 +0 +0 0 +0 +0 0 +0 +0 0 +0 +0 0 +0 +0 0 +(x^2*z1 - z0*z1^2 + z1^2)/x^3 +0 0 +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [24], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :76, in coordinates(self, threshold, basis) + +File :84, in coordinates(self, basis) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_() + 786 return self._call_with_args(x, args, kwds) + 787 +--> 788 cpdef Element _call_(self, x): + 789 """ + 790 Call method with a single argument, not implemented in the base class. + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check) + 1249 return num + 1250 if check and not den.is_unit(): + 1251 # This should probably be a ValueError. + 1252 # However, too much existing code is expecting this to throw a + 1253 # TypeError, so we decided to keep it for the time being. +-> 1254 raise TypeError("fraction must have unit denominator") + 1255 return num * den.inverse_of_unit() + +TypeError: fraction must have unit denominator +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +0 +! 0 0 +0 +! 0 0 +0 +! 0 0 +0 +! 0 0 +0 +! 0 0 +0 +! 0 0 +0 +! 0 0 +0 +! 0 0 +0 +! 0 0 +0 +! 0 0 +0 +! 0 0 +0 +! 0 0 +0 +! 0 0 +0 +! 0 0 +0 +! 0 0 +0 +! 0 0 +0 +! 0 0 +0 +! 0 0 +0 +! 0 0 +(x^2*z1 - z0*z1^2 + z1^2)/x^3 +! 0 0 +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [25], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :76, in coordinates(self, threshold, basis) + +File :84, in coordinates(self, basis) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_() + 786 return self._call_with_args(x, args, kwds) + 787 +--> 788 cpdef Element _call_(self, x): + 789 """ + 790 Call method with a single argument, not implemented in the base class. + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check) + 1249 return num + 1250 if check and not den.is_unit(): + 1251 # This should probably be a ValueError. + 1252 # However, too much existing code is expecting this to throw a + 1253 # TypeError, so we decided to keep it for the time being. +-> 1254 raise TypeError("fraction must have unit denominator") + 1255 return num * den.inverse_of_unit() + +TypeError: fraction must have unit denominator +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +? 0 +! 0 0 +? 0 +! 0 0 +? 0 +! 0 0 +? 0 +! 0 0 +? 0 +! 0 0 +? 0 +! 0 0 +? 0 +! 0 0 +? 0 +! 0 0 +? 0 +! 0 0 +? 0 +! 0 0 +? 0 +! 0 0 +? 0 +! 0 0 +? 0 +! 0 0 +? 0 +! 0 0 +? 0 +! 0 0 +? 0 +! 0 0 +? 0 +! 0 0 +? 0 +! 0 0 +? 0 +! 0 0 +? (x^2*z1 - z0*z1^2 + z1^2)/x^3 +! 0 0 +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [26], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :76, in coordinates(self, threshold, basis) + +File :84, in coordinates(self, basis) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_() + 786 return self._call_with_args(x, args, kwds) + 787 +--> 788 cpdef Element _call_(self, x): + 789 """ + 790 Call method with a single argument, not implemented in the base class. + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check) + 1249 return num + 1250 if check and not den.is_unit(): + 1251 # This should probably be a ValueError. + 1252 # However, too much existing code is expecting this to throw a + 1253 # TypeError, so we decided to keep it for the time being. +-> 1254 raise TypeError("fraction must have unit denominator") + 1255 return num * den.inverse_of_unit() + +TypeError: fraction must have unit denominator +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lTraceback (most recent call last): + + File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code + exec(code_obj, self.user_global_ns, self.user_ns) + + Input In [27] in  + load('init.sage') + + File sage/misc/persist.pyx:175 in sage.misc.persist.load + sage.repl.load.load(filename, globals()) + + File /ext/sage/9.7/src/sage/repl/load.py:272 in load + exec(preparse_file(f.read()) + "\n", globals) + + File :8 in  + + File sage/misc/persist.pyx:175 in sage.misc.persist.load + sage.repl.load.load(filename, globals()) + + File /ext/sage/9.7/src/sage/repl/load.py:272 in load + exec(preparse_file(f.read()) + "\n", globals) + + File :72 + print('!', self.f.function - rem/f_den, '!!:' quo) + ^ +SyntaxError: invalid syntax. Perhaps you forgot a comma? + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +? 0 +! 0 !!: 0 +? 0 +! 0 !!: 0 +? 0 +! 0 !!: 0 +? 0 +! 0 !!: 0 +? 0 +! 0 !!: 0 +? 0 +! 0 !!: 0 +? 0 +! 0 !!: 0 +? 0 +! 0 !!: 0 +? 0 +! 0 !!: 0 +? 0 +! 0 !!: 0 +? 0 +! 0 !!: 0 +? 0 +! 0 !!: 0 +? 0 +! 0 !!: 0 +? 0 +! 0 !!: 0 +? 0 +! 0 !!: 0 +? 0 +! 0 !!: 0 +? 0 +! 0 !!: 0 +? 0 +! 0 !!: 0 +? 0 +! 0 !!: 0 +? (x^2*z1 - z0*z1^2 + z1^2)/x^3 +! 0 !!: 0 +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [28], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :76, in coordinates(self, threshold, basis) + +File :84, in coordinates(self, basis) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_() + 786 return self._call_with_args(x, args, kwds) + 787 +--> 788 cpdef Element _call_(self, x): + 789 """ + 790 Call method with a single argument, not implemented in the base class. + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check) + 1249 return num + 1250 if check and not den.is_unit(): + 1251 # This should probably be a ValueError. + 1252 # However, too much existing code is expecting this to throw a + 1253 # TypeError, so we decided to keep it for the time being. +-> 1254 raise TypeError("fraction must have unit denominator") + 1255 return num * den.inverse_of_unit() + +TypeError: fraction must have unit denominator +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l((AS.x^2*AS.z[1] - AS.z[0]*AS.z[1]^2 + AS.z[1]^2)/AS.x^3).valuation()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l((AS.x^2*AS.z[1] - AS.z[0]*AS.z[1]^2 + AS.z[1]^2)/AS.x^3).valuation()[?7h[?12l[?25h[?25l[?7l()l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ((AS.x^2*AS.z[1] - AS.z[0]*AS.z[1]^2 + AS.z[1]^2)/AS.x^3).valuation() +[?7h[?12l[?25h[?2004l[?7h1 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +? 0 +q r: 0 0 +! 0 !!: 0 +? 0 +q r: 0 0 +! 0 !!: 0 +? 0 +q r: 0 0 +! 0 !!: 0 +? 0 +q r: 0 0 +! 0 !!: 0 +? 0 +q r: 0 0 +! 0 !!: 0 +? 0 +q r: 0 0 +! 0 !!: 0 +? 0 +q r: 0 0 +! 0 !!: 0 +? 0 +q r: 0 0 +! 0 !!: 0 +? 0 +q r: 0 0 +! 0 !!: 0 +? 0 +q r: 0 0 +! 0 !!: 0 +? 0 +q r: 0 0 +! 0 !!: 0 +? 0 +q r: 0 0 +! 0 !!: 0 +? 0 +q r: 0 0 +! 0 !!: 0 +? 0 +q r: 0 0 +! 0 !!: 0 +? 0 +q r: 0 0 +! 0 !!: 0 +? 0 +q r: 0 0 +! 0 !!: 0 +? 0 +q r: 0 0 +! 0 !!: 0 +? 0 +q r: 0 0 +! 0 !!: 0 +? 0 +q r: 0 0 +! 0 !!: 0 +? (x^2*z1 - z0*z1^2 + z1^2)/x^3 +q r: 0 x^2*z1 - z0*z1^2 + z1^2 +! 0 !!: 0 +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [30], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :77, in coordinates(self, threshold, basis) + +File :84, in coordinates(self, basis) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_() + 786 return self._call_with_args(x, args, kwds) + 787 +--> 788 cpdef Element _call_(self, x): + 789 """ + 790 Call method with a single argument, not implemented in the base class. + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check) + 1249 return num + 1250 if check and not den.is_unit(): + 1251 # This should probably be a ValueError. + 1252 # However, too much existing code is expecting this to throw a + 1253 # TypeError, so we decided to keep it for the time being. +-> 1254 raise TypeError("fraction must have unit denominator") + 1255 return num * den.inverse_of_unit() + +TypeError: fraction must have unit denominator +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +? 0 +0 q r: 0 0 +! 0 !!: 0 +? 0 +0 q r: 0 0 +! 0 !!: 0 +? 0 +0 q r: 0 0 +! 0 !!: 0 +? 0 +0 q r: 0 0 +! 0 !!: 0 +? 0 +0 q r: 0 0 +! 0 !!: 0 +? 0 +0 q r: 0 0 +! 0 !!: 0 +? 0 +0 q r: 0 0 +! 0 !!: 0 +? 0 +0 q r: 0 0 +! 0 !!: 0 +? 0 +0 q r: 0 0 +! 0 !!: 0 +? 0 +0 q r: 0 0 +! 0 !!: 0 +? 0 +0 q r: 0 0 +! 0 !!: 0 +^C--------------------------------------------------------------------------- +KeyboardInterrupt Traceback (most recent call last) +Input In [31], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :77, in coordinates(self, threshold, basis) + +File :77, in coordinates(self, basis) + +File :137, in holomorphic_differentials_basis(self, threshold) + +File :399, in holomorphic_combinations(S) + +File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() + +KeyboardInterrupt: +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l((AS.x^2*AS.z[1] - AS.z[0]*AS.z[1]^2 + AS.z[1]^2)/AS.x^3).valuation()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +? 0 +0 q r: 0 0 +! 0 !!: 0 +? 0 +0 q r: 0 0 +! 0 !!: 0 +? 0 +0 q r: 0 0 +! 0 !!: 0 +? 0 +0 q r: 0 0 +! 0 !!: 0 +? 0 +0 q r: 0 0 +! 0 !!: 0 +? 0 +0 q r: 0 0 +! 0 !!: 0 +? 0 +0 q r: 0 0 +! 0 !!: 0 +? 0 +0 q r: 0 0 +! 0 !!: 0 +? 0 +0 q r: 0 0 +! 0 !!: 0 +? 0 +0 q r: 0 0 +! 0 !!: 0 +? 0 +0 q r: 0 0 +! 0 !!: 0 +? 0 +0 q r: 0 0 +! 0 !!: 0 +? 0 +0 q r: 0 0 +! 0 !!: 0 +? 0 +0 q r: 0 0 +! 0 !!: 0 +? 0 +0 q r: 0 0 +! 0 !!: 0 +? 0 +0 q r: 0 0 +! 0 !!: 0 +? 0 +0 q r: 0 0 +! 0 !!: 0 +? 0 +0 q r: 0 0 +! 0 !!: 0 +? 0 +0 q r: 0 0 +! 0 !!: 0 +? (x^2*z1 - z0*z1^2 + z1^2)/x^3 +(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2 +! 0 !!: 0 +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [32], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :77, in coordinates(self, threshold, basis) + +File :84, in coordinates(self, basis) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_() + 786 return self._call_with_args(x, args, kwds) + 787 +--> 788 cpdef Element _call_(self, x): + 789 """ + 790 Call method with a single argument, not implemented in the base class. + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check) + 1249 return num + 1250 if check and not den.is_unit(): + 1251 # This should probably be a ValueError. + 1252 # However, too much existing code is expecting this to throw a + 1253 # TypeError, so we decided to keep it for the time being. +-> 1254 raise TypeError("fraction must have unit denominator") + 1255 return num * den.inverse_of_unit() + +TypeError: fraction must have unit denominator +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?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[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +? (x^2*z1 - z0*z1^2 + z1^2)/x^3 +(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2 +if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True +! 0 !!: 0 +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [33], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :78, in coordinates(self, threshold, basis) + +File :84, in coordinates(self, basis) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_() + 786 return self._call_with_args(x, args, kwds) + 787 +--> 788 cpdef Element _call_(self, x): + 789 """ + 790 Call method with a single argument, not implemented in the base class. + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check) + 1249 return num + 1250 if check and not den.is_unit(): + 1251 # This should probably be a ValueError. + 1252 # However, too much existing code is expecting this to throw a + 1253 # TypeError, so we decided to keep it for the time being. +-> 1254 raise TypeError("fraction must have unit denominator") + 1255 return num * den.inverse_of_unit() + +TypeError: fraction must have unit denominator +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?7h[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? (x^2*z1 - z0*z1^2 + z1^2)/x^3 +(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2 +if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True +! 0 !!: 0 +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [34], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :79, in coordinates(self, threshold, basis) + +File :84, in coordinates(self, basis) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_() + 786 return self._call_with_args(x, args, kwds) + 787 +--> 788 cpdef Element _call_(self, x): + 789 """ + 790 Call method with a single argument, not implemented in the base class. + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check) + 1249 return num + 1250 if check and not den.is_unit(): + 1251 # This should probably be a ValueError. + 1252 # However, too much existing code is expecting this to throw a + 1253 # TypeError, so we decided to keep it for the time being. +-> 1254 raise TypeError("fraction must have unit denominator") + 1255 return num * den.inverse_of_unit() + +TypeError: fraction must have unit denominator +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?7h[?7h[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?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[?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[?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(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? (x^2*z1 - z0*z1^2 + z1^2)/x^3 +(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2 +if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True +! 0 !!: 0 +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [35], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :79, in coordinates(self, threshold, basis) + +File :84, in coordinates(self, basis) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_() + 786 return self._call_with_args(x, args, kwds) + 787 +--> 788 cpdef Element _call_(self, x): + 789 """ + 790 Call method with a single argument, not implemented in the base class. + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check) + 1249 return num + 1250 if check and not den.is_unit(): + 1251 # This should probably be a ValueError. + 1252 # However, too much existing code is expecting this to throw a + 1253 # TypeError, so we decided to keep it for the time being. +-> 1254 raise TypeError("fraction must have unit denominator") + 1255 return num * den.inverse_of_unit() + +TypeError: fraction must have unit denominator +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +^C^C +KeyboardInterrupt + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? (x^2*z1 - z0*z1^2 + z1^2)/x^3 +(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2 +if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True +! 0 !!: 0 +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [37], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :79, in coordinates(self, threshold, basis) + +File :84, in coordinates(self, basis) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_() + 786 return self._call_with_args(x, args, kwds) + 787 +--> 788 cpdef Element _call_(self, x): + 789 """ + 790 Call method with a single argument, not implemented in the base class. + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check) + 1249 return num + 1250 if check and not den.is_unit(): + 1251 # This should probably be a ValueError. + 1252 # However, too much existing code is expecting this to throw a + 1253 # TypeError, so we decided to keep it for the time being. +-> 1254 raise TypeError("fraction must have unit denominator") + 1255 return num * den.inverse_of_unit() + +TypeError: fraction must have unit denominator +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? (x^2*z1 - z0*z1^2 + z1^2)/x^3 +(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2 +if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True +! 0 !!: 0 +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [38], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :79, in coordinates(self, threshold, basis) + +File :84, in coordinates(self, basis) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_() + 786 return self._call_with_args(x, args, kwds) + 787 +--> 788 cpdef Element _call_(self, x): + 789 """ + 790 Call method with a single argument, not implemented in the base class. + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check) + 1249 return num + 1250 if check and not den.is_unit(): + 1251 # This should probably be a ValueError. + 1252 # However, too much existing code is expecting this to throw a + 1253 # TypeError, so we decided to keep it for the time being. +-> 1254 raise TypeError("fraction must have unit denominator") + 1255 return num * den.inverse_of_unit() + +TypeError: fraction must have unit denominator +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?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(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +^C--------------------------------------------------------------------------- +KeyboardInterrupt Traceback (most recent call last) +Input In [39], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :56, in coordinates(self, threshold, basis) + +File /ext/sage/9.7/src/sage/misc/functional.py:585, in symbolic_sum(expression, *args, **kwds) + 583 return expression.sum(*args, **kwds) + 584 elif max(len(args),len(kwds)) <= 1: +--> 585 return sum(expression, *args, **kwds) + 586 else: + 587 from sage.symbolic.ring import SR + +File :56, in (.0) + +File :47, in __mul__(self, other) + +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[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit() +[?7h[?12l[?25h[?2004l +]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage +┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.7, Release Date: 2022-09-19 │ +│ Using Python 3.10.5. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? (x^2*z1 - z0*z1^2 + z1^2)/x^3 +(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2 +if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True +! 0 !!: 0 +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [1], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :79, in coordinates(self, threshold, basis) + +File :84, in coordinates(self, basis) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_() + 786 return self._call_with_args(x, args, kwds) + 787 +--> 788 cpdef Element _call_(self, x): + 789 """ + 790 Call method with a single argument, not implemented in the base class. + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check) + 1249 return num + 1250 if check and not den.is_unit(): + 1251 # This should probably be a ValueError. + 1252 # However, too much existing code is expecting this to throw a + 1253 # TypeError, so we decided to keep it for the time being. +-> 1254 raise TypeError("fraction must have unit denominator") + 1255 return num * den.inverse_of_unit() + +TypeError: fraction must have unit denominator +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? (x^2*z1 - z0*z1^2 + z1^2)/x^3 +(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2 +if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True +! 0 !!: 0 +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [2], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :79, in coordinates(self, threshold, basis) + +File :84, in coordinates(self, basis) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_() + 786 return self._call_with_args(x, args, kwds) + 787 +--> 788 cpdef Element _call_(self, x): + 789 """ + 790 Call method with a single argument, not implemented in the base class. + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check) + 1249 return num + 1250 if check and not den.is_unit(): + 1251 # This should probably be a ValueError. + 1252 # However, too much existing code is expecting this to throw a + 1253 # TypeError, so we decided to keep it for the time being. +-> 1254 raise TypeError("fraction must have unit denominator") + 1255 return num * den.inverse_of_unit() + +TypeError: fraction must have unit denominator +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 + +? (x^2*z1 - z0*z1^2 + z1^2)/x^3 +(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2 +if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True +! 0 !!: 0 +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [3], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :79, in coordinates(self, threshold, basis) + +File :84, in coordinates(self, basis) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_() + 786 return self._call_with_args(x, args, kwds) + 787 +--> 788 cpdef Element _call_(self, x): + 789 """ + 790 Call method with a single argument, not implemented in the base class. + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check) + 1249 return num + 1250 if check and not den.is_unit(): + 1251 # This should probably be a ValueError. + 1252 # However, too much existing code is expecting this to throw a + 1253 # TypeError, so we decided to keep it for the time being. +-> 1254 raise TypeError("fraction must have unit denominator") + 1255 return num * den.inverse_of_unit() + +TypeError: fraction must have unit denominator +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?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 9.7, Release Date: 2022-09-19 │ +│ Using Python 3.10.5. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004lWARNING: your terminal doesn't support cursor position requests (CPR). +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +nowe!!!! ( (1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +nowe!!!! ( (z1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +nowe!!!! ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +nowe!!!! ( (z0 + 1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +nowe!!!! ( (z0*z1 + z1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +nowe!!!! ( (z0^2 - z0 + 1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +nowe!!!! ( (x) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +nowe!!!! ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +nowe!!!! ( (x*z0 + x) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +nowe!!!! ( (x^2) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +nowe!!!! ( ((-x^4 - z1)/x^2) * dx, z1/x ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +nowe!!!! ( ((-z1^2)/x^2) * dx, z1^2/x ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +nowe!!!! ( ((x^2*z1 - z0*z1 - z1)/x^2) * dx, (z0*z1 + z1)/x ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +nowe!!!! ( ((x^4*z0 + x^2*z0^2*z1 + x^4 - x^2*z0*z1 + x^2*z1^2 + x^2*z1 - z0*z1^2 - z1^2)/x^2) * dx, (z0*z1^2 + z1^2)/x ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +nowe!!!! ( ((-x^2*z0*z1 - x^2*z1 - z0^2*z1 + z0*z1 - z1)/x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +nowe!!!! ( ((-z0^2*z1^2 + z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +nowe!!!! ( ((-x^4*z0^2 + x^4*z0 + x^4*z1 - x^4 + z1^2)/x^3) * dx, z1^2/x^2 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +nowe!!!! ( ((x^2*z1^2 + z0*z1^2 + z1^2)/x^3) * dx, (z0*z1^2 + z1^2)/x^2 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +nowe!!!! ( ((x^4*z0^2 - x^4*z0 - x^2*z0*z1^2 + x^4 - x^2*z1^2 + z0^2*z1^2 - z0*z1^2 + z1^2)/x^3) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +nowe!!!! ( ((-z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) +? (x^2*z1 - z0*z1^2 + z1^2)/x^3 +(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2 +if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True +! 0 !!: 0 +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [1], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :79, in coordinates(self, threshold, basis) + +File :84, in coordinates(self, basis) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_() + 786 return self._call_with_args(x, args, kwds) + 787 +--> 788 cpdef Element _call_(self, x): + 789 """ + 790 Call method with a single argument, not implemented in the base class. + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check) + 1249 return num + 1250 if check and not den.is_unit(): + 1251 # This should probably be a ValueError. + 1252 # However, too much existing code is expecting this to throw a + 1253 # TypeError, so we decided to keep it for the time being. +-> 1254 raise TypeError("fraction must have unit denominator") + 1255 return num * den.inverse_of_unit() + +TypeError: fraction must have unit denominator +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +nowe!!!! ( (1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (1) * dx, 0 ) +nowe!!!! ( (z1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (z1) * dx, 0 ) +nowe!!!! ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) +nowe!!!! ( (z0 + 1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (z0 + 1) * dx, 0 ) +nowe!!!! ( (z0*z1 + z1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (z0*z1 + z1) * dx, 0 ) +nowe!!!! ( (z0^2 - z0 + 1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (z0^2 - z0 + 1) * dx, 0 ) +nowe!!!! ( (x) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (x) * dx, 0 ) +nowe!!!! ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) +nowe!!!! ( (x*z0 + x) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (x*z0 + x) * dx, 0 ) +nowe!!!! ( (x^2) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (x^2) * dx, 0 ) +nowe!!!! ( ((-x^4 - z1)/x^2) * dx, z1/x ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (0) * dx, 0 ) +nowe!!!! ( ((-z1^2)/x^2) * dx, z1^2/x ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (0) * dx, 0 ) +nowe!!!! ( ((x^2*z1 - z0*z1 - z1)/x^2) * dx, (z0*z1 + z1)/x ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (x^2) * dx, 0 ) +nowe!!!! ( ((x^4*z0 + x^2*z0^2*z1 + x^4 - x^2*z0*z1 + x^2*z1^2 + x^2*z1 - z0*z1^2 - z1^2)/x^2) * dx, (z0*z1^2 + z1^2)/x ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (x^2 - z0*z1 + z1) * dx, 0 ) +nowe!!!! ( ((-x^2*z0*z1 - x^2*z1 - z0^2*z1 + z0*z1 - z1)/x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (x^2) * dx, 0 ) +nowe!!!! ( ((-z0^2*z1^2 + z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 ) +nowe!!!! ( ((-x^4*z0^2 + x^4*z0 + x^4*z1 - x^4 + z1^2)/x^3) * dx, z1^2/x^2 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (x*z0 - x) * dx, 0 ) +nowe!!!! ( ((x^2*z1^2 + z0*z1^2 + z1^2)/x^3) * dx, (z0*z1^2 + z1^2)/x^2 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (x*z0^2 - x*z1) * dx, 0 ) +nowe!!!! ( ((x^4*z0^2 - x^4*z0 - x^2*z0*z1^2 + x^4 - x^2*z1^2 + z0^2*z1^2 - z0*z1^2 + z1^2)/x^3) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (x*z0^2 - x*z0 - x*z1 + x) * dx, 0 ) +nowe!!!! ( ((-z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) +? (x^2*z1 - z0*z1^2 + z1^2)/x^3 +(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2 +if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True +! 0 !!: 0 +selfik ( ((-x^4 - z1^2 - z1)/x^2) * dx, 0 ) +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [2], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :80, in coordinates(self, threshold, basis) + +File :84, in coordinates(self, basis) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_() + 786 return self._call_with_args(x, args, kwds) + 787 +--> 788 cpdef Element _call_(self, x): + 789 """ + 790 Call method with a single argument, not implemented in the base class. + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check) + 1249 return num + 1250 if check and not den.is_unit(): + 1251 # This should probably be a ValueError. + 1252 # However, too much existing code is expecting this to throw a + 1253 # TypeError, so we decided to keep it for the time being. +-> 1254 raise TypeError("fraction must have unit denominator") + 1255 return num * den.inverse_of_unit() + +TypeError: fraction must have unit denominator +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +nowe!!!! ( (1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (1) * dx, 0 ) +nowe!!!! ( (z1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (z1) * dx, 0 ) +nowe!!!! ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) +nowe!!!! ( (z0 + 1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (z0 + 1) * dx, 0 ) +nowe!!!! ( (z0*z1 + z1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (z0*z1 + z1) * dx, 0 ) +nowe!!!! ( (z0^2 - z0 + 1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (z0^2 - z0 + 1) * dx, 0 ) +nowe!!!! ( (x) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (x) * dx, 0 ) +nowe!!!! ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) +nowe!!!! ( (x*z0 + x) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (x*z0 + x) * dx, 0 ) +nowe!!!! ( (x^2) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (x^2) * dx, 0 ) +nowe!!!! ( ((-x^4 - z1)/x^2) * dx, z1/x ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (0) * dx, 0 ) +nowe!!!! ( ((-z1^2)/x^2) * dx, z1^2/x ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (0) * dx, 0 ) +nowe!!!! ( ((x^2*z1 - z0*z1 - z1)/x^2) * dx, (z0*z1 + z1)/x ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (x^2) * dx, 0 ) +nowe!!!! ( ((x^4*z0 + x^2*z0^2*z1 + x^4 - x^2*z0*z1 + x^2*z1^2 + x^2*z1 - z0*z1^2 - z1^2)/x^2) * dx, (z0*z1^2 + z1^2)/x ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (x^2 - z0*z1 + z1) * dx, 0 ) +nowe!!!! ( ((-x^2*z0*z1 - x^2*z1 - z0^2*z1 + z0*z1 - z1)/x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (x^2) * dx, 0 ) +nowe!!!! ( ((-z0^2*z1^2 + z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 ) +nowe!!!! ( ((-x^4*z0^2 + x^4*z0 + x^4*z1 - x^4 + z1^2)/x^3) * dx, z1^2/x^2 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (x*z0 - x) * dx, 0 ) +nowe!!!! ( ((x^2*z1^2 + z0*z1^2 + z1^2)/x^3) * dx, (z0*z1^2 + z1^2)/x^2 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (x*z0^2 - x*z1) * dx, 0 ) +nowe!!!! ( ((x^4*z0^2 - x^4*z0 - x^2*z0*z1^2 + x^4 - x^2*z1^2 + z0^2*z1^2 - z0*z1^2 + z1^2)/x^3) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (x*z0^2 - x*z0 - x*z1 + x) * dx, 0 ) +nowe!!!! ( ((-z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) +? (x^2*z1 - z0*z1^2 + z1^2)/x^3 +(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2 +if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True +! 0 !!: 0 +selfik ( ((-x^4 - z1^2 - z1)/x^2) * dx, 0 ) +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [3], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :80, in coordinates(self, threshold, basis) + +File :84, in coordinates(self, basis) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_() + 786 return self._call_with_args(x, args, kwds) + 787 +--> 788 cpdef Element _call_(self, x): + 789 """ + 790 Call method with a single argument, not implemented in the base class. + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check) + 1249 return num + 1250 if check and not den.is_unit(): + 1251 # This should probably be a ValueError. + 1252 # However, too much existing code is expecting this to throw a + 1253 # TypeError, so we decided to keep it for the time being. +-> 1254 raise TypeError("fraction must have unit denominator") + 1255 return num * den.inverse_of_unit() + +TypeError: fraction must have unit denominator +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +nowe!!!! ( (1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (1) * dx, 0 ) +nowe!!!! ( (z1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (z1) * dx, 0 ) +nowe!!!! ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) +nowe!!!! ( (z0 + 1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (z0 + 1) * dx, 0 ) +nowe!!!! ( (z0*z1 + z1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (z0*z1 + z1) * dx, 0 ) +nowe!!!! ( (z0^2 - z0 + 1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (z0^2 - z0 + 1) * dx, 0 ) +nowe!!!! ( (x) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (x) * dx, 0 ) +nowe!!!! ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) +nowe!!!! ( (x*z0 + x) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (x*z0 + x) * dx, 0 ) +nowe!!!! ( (x^2) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (x^2) * dx, 0 ) +nowe!!!! ( ((-x^4 - z1)/x^2) * dx, z1/x ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (0) * dx, 0 ) +nowe!!!! ( ((-z1^2)/x^2) * dx, z1^2/x ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (0) * dx, 0 ) +nowe!!!! ( ((x^2*z1 - z0*z1 - z1)/x^2) * dx, (z0*z1 + z1)/x ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (x^2) * dx, 0 ) +nowe!!!! ( ((x^4*z0 + x^2*z0^2*z1 + x^4 - x^2*z0*z1 + x^2*z1^2 + x^2*z1 - z0*z1^2 - z1^2)/x^2) * dx, (z0*z1^2 + z1^2)/x ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (x^2 - z0*z1 + z1) * dx, 0 ) +nowe!!!! ( ((-x^2*z0*z1 - x^2*z1 - z0^2*z1 + z0*z1 - z1)/x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (x^2) * dx, 0 ) +nowe!!!! ( ((-z0^2*z1^2 + z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 ) +nowe!!!! ( ((-x^4*z0^2 + x^4*z0 + x^4*z1 - x^4 + z1^2)/x^3) * dx, z1^2/x^2 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (x*z0 - x) * dx, 0 ) +nowe!!!! ( ((x^2*z1^2 + z0*z1^2 + z1^2)/x^3) * dx, (z0*z1^2 + z1^2)/x^2 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (x*z0^2 - x*z1) * dx, 0 ) +nowe!!!! ( ((x^4*z0^2 - x^4*z0 - x^2*z0*z1^2 + x^4 - x^2*z1^2 + z0^2*z1^2 - z0*z1^2 + z1^2)/x^3) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (x*z0^2 - x*z0 - x*z1 + x) * dx, 0 ) +nowe!!!! ( ((-z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) +? (x^2*z1 - z0*z1^2 + z1^2)/x^3 +(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2 +if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True +! 0 !!: 0 +selfik ( ((-x^4 - z1^2 - z1)/x^2) * dx, 0 ) +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [4], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :80, in coordinates(self, threshold, basis) + +File :84, in coordinates(self, basis) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_() + 786 return self._call_with_args(x, args, kwds) + 787 +--> 788 cpdef Element _call_(self, x): + 789 """ + 790 Call method with a single argument, not implemented in the base class. + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check) + 1249 return num + 1250 if check and not den.is_unit(): + 1251 # This should probably be a ValueError. + 1252 # However, too much existing code is expecting this to throw a + 1253 # TypeError, so we decided to keep it for the time being. +-> 1254 raise TypeError("fraction must have unit denominator") + 1255 return num * den.inverse_of_unit() + +TypeError: fraction must have unit denominator +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?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[?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[?7lsage:  +[?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[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +nowe!!!! ( (1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (1) * dx, 0 ) +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (z1) * dx, 0 ) +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0 + 1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (z0 + 1) * dx, 0 ) +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0*z1 + z1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (z0*z1 + z1) * dx, 0 ) +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0^2 - z0 + 1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (z0^2 - z0 + 1) * dx, 0 ) +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (x) * dx, 0 ) +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x*z0 + x) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (x*z0 + x) * dx, 0 ) +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (x^2) * dx, 0 ) +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-x^4 - z1)/x^2) * dx, z1/x ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (0) * dx, 0 ) +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-z1^2)/x^2) * dx, z1^2/x ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (0) * dx, 0 ) +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((x^2*z1 - z0*z1 - z1)/x^2) * dx, (z0*z1 + z1)/x ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (x^2) * dx, 0 ) +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((x^4*z0 + x^2*z0^2*z1 + x^4 - x^2*z0*z1 + x^2*z1^2 + x^2*z1 - z0*z1^2 - z1^2)/x^2) * dx, (z0*z1^2 + z1^2)/x ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (x^2 - z0*z1 + z1) * dx, 0 ) +(x^2 - z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-x^2*z0*z1 - x^2*z1 - z0^2*z1 + z0*z1 - z1)/x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (x^2) * dx, 0 ) +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-z0^2*z1^2 + z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 ) +(x^2*z0 + z0^2*z1 + z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-x^4*z0^2 + x^4*z0 + x^4*z1 - x^4 + z1^2)/x^3) * dx, z1^2/x^2 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (x*z0 - x) * dx, 0 ) +(x*z0 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((x^2*z1^2 + z0*z1^2 + z1^2)/x^3) * dx, (z0*z1^2 + z1^2)/x^2 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (x*z0^2 - x*z1) * dx, 0 ) +(x*z0^2 - x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((x^4*z0^2 - x^4*z0 - x^2*z0*z1^2 + x^4 - x^2*z1^2 + z0^2*z1^2 - z0*z1^2 + z1^2)/x^3) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) +? 0 +0 q r: 0 0 +if 0 True +! 0 !!: 0 +selfik ( (x*z0^2 - x*z0 - x*z1 + x) * dx, 0 ) +(x*z0^2 - x*z0 - x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) +? (x^2*z1 - z0*z1^2 + z1^2)/x^3 +(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2 +if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True +! 0 !!: 0 +selfik ( ((-x^4 - z1^2 - z1)/x^2) * dx, 0 ) +((-x^4 - z1^2 - z1)/x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [5], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :80, in coordinates(self, threshold, basis) + +File :85, in coordinates(self, basis) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_() + 786 return self._call_with_args(x, args, kwds) + 787 +--> 788 cpdef Element _call_(self, x): + 789 """ + 790 Call method with a single argument, not implemented in the base class. + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check) + 1249 return num + 1250 if check and not den.is_unit(): + 1251 # This should probably be a ValueError. + 1252 # However, too much existing code is expecting this to throw a + 1253 # TypeError, so we decided to keep it for the time being. +-> 1254 raise TypeError("fraction must have unit denominator") + 1255 return num * den.inverse_of_unit() + +TypeError: fraction must have unit denominator +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +nowe!!!! ( (1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (1) * dx, 0 ) +--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Input In [6], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :77, in coordinates(self, threshold, basis) + +File :133, in diffn(self) + +File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() + 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' + 493 """ +--> 494 return self.getattr_from_category(name) + 495 + 496 cdef getattr_from_category(self, name): + +File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() + 505 else: + 506 cls = P._abstract_element_class +--> 507 return getattr_from_other_class(self, cls, name) + 508 + 509 def __dir__(self): + +File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() + 359 dummy_error_message.cls = type(self) + 360 dummy_error_message.name = name +--> 361 raise AttributeError(dummy_error_message) + 362 attribute = attr + 363 # Check for a descriptor (__get__ in Python) + +AttributeError: 'sage.rings.integer.Integer' object has no attribute 'derivative' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +nowe!!!! ( (1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (1) * dx, 0 ) +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (z1) * dx, 0 ) +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0 + 1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (z0 + 1) * dx, 0 ) +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0*z1 + z1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (z0*z1 + z1) * dx, 0 ) +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0^2 - z0 + 1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (z0^2 - z0 + 1) * dx, 0 ) +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (x) * dx, 0 ) +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x*z0 + x) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (x*z0 + x) * dx, 0 ) +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (x^2) * dx, 0 ) +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-x^4 - z1)/x^2) * dx, z1/x ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (0) * dx, 0 ) +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-z1^2)/x^2) * dx, z1^2/x ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (0) * dx, 0 ) +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((x^2*z1 - z0*z1 - z1)/x^2) * dx, (z0*z1 + z1)/x ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (x^2) * dx, 0 ) +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((x^4*z0 + x^2*z0^2*z1 + x^4 - x^2*z0*z1 + x^2*z1^2 + x^2*z1 - z0*z1^2 - z1^2)/x^2) * dx, (z0*z1^2 + z1^2)/x ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (x^2 - z0*z1 + z1) * dx, 0 ) +(x^2 - z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-x^2*z0*z1 - x^2*z1 - z0^2*z1 + z0*z1 - z1)/x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (x^2) * dx, 0 ) +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-z0^2*z1^2 + z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 ) +(x^2*z0 + z0^2*z1 + z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-x^4*z0^2 + x^4*z0 + x^4*z1 - x^4 + z1^2)/x^3) * dx, z1^2/x^2 ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (x*z0 - x) * dx, 0 ) +(x*z0 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((x^2*z1^2 + z0*z1^2 + z1^2)/x^3) * dx, (z0*z1^2 + z1^2)/x^2 ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (x*z0^2 - x*z1) * dx, 0 ) +(x*z0^2 - x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((x^4*z0^2 - x^4*z0 - x^2*z0*z1^2 + x^4 - x^2*z1^2 + z0^2*z1^2 - z0*z1^2 + z1^2)/x^3) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (x*z0^2 - x*z0 - x*z1 + x) * dx, 0 ) +(x*z0^2 - x*z0 - x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) +? (x^2*z1 - z0*z1^2 + z1^2)/x^3 +(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2 +if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True +selfik ( ((-x^4 - z1^2 - z1)/x^2) * dx, 0 ) +((-x^4 - z1^2 - z1)/x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [7], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :80, in coordinates(self, threshold, basis) + +File :85, in coordinates(self, basis) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_() + 786 return self._call_with_args(x, args, kwds) + 787 +--> 788 cpdef Element _call_(self, x): + 789 """ + 790 Call method with a single argument, not implemented in the base class. + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check) + 1249 return num + 1250 if check and not den.is_unit(): + 1251 # This should probably be a ValueError. + 1252 # However, too much existing code is expecting this to throw a + 1253 # TypeError, so we decided to keep it for the time being. +-> 1254 raise TypeError("fraction must have unit denominator") + 1255 return num * den.inverse_of_unit() + +TypeError: fraction must have unit denominator +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +nowe!!!! ( (1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (1) * dx, 0 ) +--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Input In [8], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :78, in coordinates(self, threshold, basis) + +File :133, in diffn(self) + +AttributeError: 'as_function' object has no attribute 'derivative' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l((AS.x^2*AS.z[1] - AS.z[0]*AS.z[1]^2 + AS.z[1]^2)/AS.x^3).valuation()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +nowe!!!! ( (1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (1) * dx, 0 ) +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (z1) * dx, 0 ) +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0 + 1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (z0 + 1) * dx, 0 ) +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0*z1 + z1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (z0*z1 + z1) * dx, 0 ) +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0^2 - z0 + 1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (z0^2 - z0 + 1) * dx, 0 ) +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (x) * dx, 0 ) +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x*z0 + x) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (x*z0 + x) * dx, 0 ) +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (x^2) * dx, 0 ) +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-x^4 - z1)/x^2) * dx, z1/x ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (0) * dx, 0 ) +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-z1^2)/x^2) * dx, z1^2/x ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (0) * dx, 0 ) +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((x^2*z1 - z0*z1 - z1)/x^2) * dx, (z0*z1 + z1)/x ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (x^2) * dx, 0 ) +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((x^4*z0 + x^2*z0^2*z1 + x^4 - x^2*z0*z1 + x^2*z1^2 + x^2*z1 - z0*z1^2 - z1^2)/x^2) * dx, (z0*z1^2 + z1^2)/x ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (x^2 - z0*z1 + z1) * dx, 0 ) +(x^2 - z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-x^2*z0*z1 - x^2*z1 - z0^2*z1 + z0*z1 - z1)/x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (x^2) * dx, 0 ) +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-z0^2*z1^2 + z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 ) +(x^2*z0 + z0^2*z1 + z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-x^4*z0^2 + x^4*z0 + x^4*z1 - x^4 + z1^2)/x^3) * dx, z1^2/x^2 ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (x*z0 - x) * dx, 0 ) +(x*z0 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((x^2*z1^2 + z0*z1^2 + z1^2)/x^3) * dx, (z0*z1^2 + z1^2)/x^2 ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (x*z0^2 - x*z1) * dx, 0 ) +(x*z0^2 - x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((x^4*z0^2 - x^4*z0 - x^2*z0*z1^2 + x^4 - x^2*z1^2 + z0^2*z1^2 - z0*z1^2 + z1^2)/x^3) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (x*z0^2 - x*z0 - x*z1 + x) * dx, 0 ) +(x*z0^2 - x*z0 - x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) +? (x^2*z1 - z0*z1^2 + z1^2)/x^3 +(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2 +if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True +selfik ( ((-x^4 - z1^2 - z1)/x^2) * dx, 0 ) +((-x^4 - z1^2 - z1)/x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [9], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :80, in coordinates(self, threshold, basis) + +File :85, in coordinates(self, basis) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_() + 786 return self._call_with_args(x, args, kwds) + 787 +--> 788 cpdef Element _call_(self, x): + 789 """ + 790 Call method with a single argument, not implemented in the base class. + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check) + 1249 return num + 1250 if check and not den.is_unit(): + 1251 # This should probably be a ValueError. + 1252 # However, too much existing code is expecting this to throw a + 1253 # TypeError, so we decided to keep it for the time being. +-> 1254 raise TypeError("fraction must have unit denominator") + 1255 return num * den.inverse_of_unit() + +TypeError: fraction must have unit denominator +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?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:  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[?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +nowe!!!! ( (1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (1) * dx, 0 ) +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (z1) * dx, 0 ) +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0 + 1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (z0 + 1) * dx, 0 ) +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0*z1 + z1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (z0*z1 + z1) * dx, 0 ) +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0^2 - z0 + 1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (z0^2 - z0 + 1) * dx, 0 ) +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (x) * dx, 0 ) +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x*z0 + x) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (x*z0 + x) * dx, 0 ) +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (x^2) * dx, 0 ) +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-x^4 - z1)/x^2) * dx, z1/x ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (0) * dx, 0 ) +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-z1^2)/x^2) * dx, z1^2/x ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (0) * dx, 0 ) +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((x^2*z1 - z0*z1 - z1)/x^2) * dx, (z0*z1 + z1)/x ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (x^2) * dx, 0 ) +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((x^4*z0 + x^2*z0^2*z1 + x^4 - x^2*z0*z1 + x^2*z1^2 + x^2*z1 - z0*z1^2 - z1^2)/x^2) * dx, (z0*z1^2 + z1^2)/x ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (x^2 - z0*z1 + z1) * dx, 0 ) +(x^2 - z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-x^2*z0*z1 - x^2*z1 - z0^2*z1 + z0*z1 - z1)/x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (x^2) * dx, 0 ) +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-z0^2*z1^2 + z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 ) +(x^2*z0 + z0^2*z1 + z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-x^4*z0^2 + x^4*z0 + x^4*z1 - x^4 + z1^2)/x^3) * dx, z1^2/x^2 ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (x*z0 - x) * dx, 0 ) +(x*z0 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((x^2*z1^2 + z0*z1^2 + z1^2)/x^3) * dx, (z0*z1^2 + z1^2)/x^2 ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (x*z0^2 - x*z1) * dx, 0 ) +(x*z0^2 - x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((x^4*z0^2 - x^4*z0 - x^2*z0*z1^2 + x^4 - x^2*z1^2 + z0^2*z1^2 - z0*z1^2 + z1^2)/x^3) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) +? 0 +0 q r: 0 0 +if 0 True +selfik ( (x*z0^2 - x*z0 - x*z1 + x) * dx, 0 ) +(x*z0^2 - x*z0 - x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) +? (x^2*z1 - z0*z1^2 + z1^2)/x^3 +(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2 +if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True +selfik ( ((-x^4 - z1^2 - z1)/x^2) * dx, 0 ) +((-x^4 - z1^2 - z1)/x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [10], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :80, in coordinates(self, threshold, basis) + +File :85, in coordinates(self, basis) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_() + 786 return self._call_with_args(x, args, kwds) + 787 +--> 788 cpdef Element _call_(self, x): + 789 """ + 790 Call method with a single argument, not implemented in the base class. + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check) + 1249 return num + 1250 if check and not den.is_unit(): + 1251 # This should probably be a ValueError. + 1252 # However, too much existing code is expecting this to throw a + 1253 # TypeError, so we decided to keep it for the time being. +-> 1254 raise TypeError("fraction must have unit denominator") + 1255 return num * den.inverse_of_unit() + +TypeError: fraction must have unit denominator +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l((AS.x^2*AS.z[1] - AS.z[0]*AS.z[1]^2 + AS.z[1]^2)/AS.x^3).valuation()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l((AS.x^2*AS.z[1] - AS.z[0]*AS.z[1]^2 + AS.z[1]^2)/AS.x^3).valuation()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l((AS.x^2*AS.z[1] - AS.z[0]*AS.z[1]^2 + AS.z[1]^2)/AS.x^3).valuation()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l[?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(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +nowe!!!! ( (1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (1) * dx +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (z1) * dx +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0 + 1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (z0 + 1) * dx +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0*z1 + z1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (z0*z1 + z1) * dx +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0^2 - z0 + 1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (z0^2 - z0 + 1) * dx +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (x) * dx +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x*z0 + x) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (x*z0 + x) * dx +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-x^4 - z1)/x^2) * dx, z1/x ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-z1^2)/x^2) * dx, z1^2/x ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((x^2*z1 - z0*z1 - z1)/x^2) * dx, (z0*z1 + z1)/x ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((x^4*z0 + x^2*z0^2*z1 + x^4 - x^2*z0*z1 + x^2*z1^2 + x^2*z1 - z0*z1^2 - z1^2)/x^2) * dx, (z0*z1^2 + z1^2)/x ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (x^2 - z0*z1 + z1) * dx +(x^2 - z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-x^2*z0*z1 - x^2*z1 - z0^2*z1 + z0*z1 - z1)/x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-z0^2*z1^2 + z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (x^2*z0 + z0^2*z1 + z1^2) * dx +(x^2*z0 + z0^2*z1 + z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-x^4*z0^2 + x^4*z0 + x^4*z1 - x^4 + z1^2)/x^3) * dx, z1^2/x^2 ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (x*z0 - x) * dx +(x*z0 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((x^2*z1^2 + z0*z1^2 + z1^2)/x^3) * dx, (z0*z1^2 + z1^2)/x^2 ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (x*z0^2 - x*z1) * dx +(x*z0^2 - x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((x^4*z0^2 - x^4*z0 - x^2*z0*z1^2 + x^4 - x^2*z1^2 + z0^2*z1^2 - z0*z1^2 + z1^2)/x^3) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (x*z0^2 - x*z0 - x*z1 + x) * dx +(x*z0^2 - x*z0 - x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) +? (x^2*z1 - z0*z1^2 + z1^2)/x^3 +(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2 +if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True +hol_form ((-x^4 - z1^2 - z1)/x^2) * dx +((-x^4 - z1^2 - z1)/x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [11], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :80, in coordinates(self, threshold, basis) + +File :85, in coordinates(self, basis) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_() + 786 return self._call_with_args(x, args, kwds) + 787 +--> 788 cpdef Element _call_(self, x): + 789 """ + 790 Call method with a single argument, not implemented in the base class. + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check) + 1249 return num + 1250 if check and not den.is_unit(): + 1251 # This should probably be a ValueError. + 1252 # However, too much existing code is expecting this to throw a + 1253 # TypeError, so we decided to keep it for the time being. +-> 1254 raise TypeError("fraction must have unit denominator") + 1255 return num * den.inverse_of_unit() + +TypeError: fraction must have unit denominator +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.z[1]^2/AS.x*AS.dx[?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[?7llomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis() +[?7h[?12l[?25h[?2004l[?7h[(1) * dx, + (z1) * dx, + (x^2*z0 + z0^2*z1 + z1^2) * dx, + (z0) * dx, + (z0*z1) * dx, + (z0^2) * dx, + (x) * dx, + (-x*z0^2 + x*z1) * dx, + (x*z0) * dx, + (x^2) * dx] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage +┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.7, Release Date: 2022-09-19 │ +│ Using Python 3.10.5. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +nowe!!!! ( (1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (1) * dx +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (z1) * dx +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0 + 1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (z0 + 1) * dx +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0*z1 + z1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (z0*z1 + z1) * dx +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0^2 - z0 + 1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (z0^2 - z0 + 1) * dx +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (x) * dx +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x*z0 + x) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (x*z0 + x) * dx +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-x^4 - z1)/x^2) * dx, z1/x ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-z1^2)/x^2) * dx, z1^2/x ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((x^2*z1 - z0*z1 - z1)/x^2) * dx, (z0*z1 + z1)/x ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((x^4*z0 + x^2*z0^2*z1 + x^4 - x^2*z0*z1 + x^2*z1^2 + x^2*z1 - z0*z1^2 - z1^2)/x^2) * dx, (z0*z1^2 + z1^2)/x ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (x^2 - z0*z1 + z1) * dx +(x^2 - z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-x^2*z0*z1 - x^2*z1 - z0^2*z1 + z0*z1 - z1)/x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-z0^2*z1^2 + z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (x^2*z0 + z0^2*z1 + z1^2) * dx +(x^2*z0 + z0^2*z1 + z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-x^4*z0^2 + x^4*z0 + x^4*z1 - x^4 + z1^2)/x^3) * dx, z1^2/x^2 ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (x*z0 - x) * dx +(x*z0 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((x^2*z1^2 + z0*z1^2 + z1^2)/x^3) * dx, (z0*z1^2 + z1^2)/x^2 ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (x*z0^2 - x*z1) * dx +(x*z0^2 - x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((x^4*z0^2 - x^4*z0 - x^2*z0*z1^2 + x^4 - x^2*z1^2 + z0^2*z1^2 - z0*z1^2 + z1^2)/x^3) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (x*z0^2 - x*z0 - x*z1 + x) * dx +(x*z0^2 - x*z0 - x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) +? (x^2*z1 - z0*z1^2 + z1^2)/x^3 +(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2 +if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True +hol_form ((-x^4 - z1^2 - z1)/x^2) * dx +((-x^4 - z1^2 - z1)/x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [1], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :80, in coordinates(self, threshold, basis) + +File :85, in coordinates(self, basis) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_() + 786 return self._call_with_args(x, args, kwds) + 787 +--> 788 cpdef Element _call_(self, x): + 789 """ + 790 Call method with a single argument, not implemented in the base class. + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check) + 1249 return num + 1250 if check and not den.is_unit(): + 1251 # This should probably be a ValueError. + 1252 # However, too much existing code is expecting this to throw a + 1253 # TypeError, so we decided to keep it for the time being. +-> 1254 raise TypeError("fraction must have unit denominator") + 1255 return num * den.inverse_of_unit() + +TypeError: fraction must have unit denominator +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = AS.holomorphic_differentials_basis()[1][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l AS.holomorphic_differentials_basis()[1][?7h[?12l[?25h[?25l[?7lsage: om = AS.holomorphic_differentials_basis()[1] +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = Rxy(x^2 + y^3)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = Rxy(x^2 + y^3)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?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[?7l[?7h[?12l[?25h[?25l[?7l[?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[?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[?7lo[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lsage: f = AS.cohomology_of s + sage sage_globals sageobj save_session scilab   + sage0 sage_input sample %sc %%script   + sage0_version sage_mode sandpiles scatter_plot search_def > + sage_eval sage_wraps save schonheim search_doc   + [?7h[?12l[?25h[?25l[?7l + + + +[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_of_structure_sheaf_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: f = AS.cohomology_of_structure_sheaf_basis()[1] +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + + [?7h[?12l[?25h[?25l[?7lom = AS.holomorphic_differentials_basis()[1][?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lrre_duality_pairing[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.serre_duality_pairing(f) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  + + + [?7h[?12l[?25h[?25l[?7lom.serre_duality_pairing(f)[?7h[?12l[?25h[?25l[?7lf = AS.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7lom = AS.holomorphic_differentials_basis()[1][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +nowe!!!! ( (1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (1) * dx +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (z1) * dx +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0 + 1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (z0 + 1) * dx +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0*z1 + z1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (z0*z1 + z1) * dx +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0^2 - z0 + 1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (z0^2 - z0 + 1) * dx +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (x) * dx +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x*z0 + x) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (x*z0 + x) * dx +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-x^4 - z1)/x^2) * dx, z1/x ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-z1^2)/x^2) * dx, z1^2/x ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((x^2*z1 - z0*z1 - z1)/x^2) * dx, (z0*z1 + z1)/x ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((x^4*z0 + x^2*z0^2*z1 + x^4 - x^2*z0*z1 + x^2*z1^2 + x^2*z1 - z0*z1^2 - z1^2)/x^2) * dx, (z0*z1^2 + z1^2)/x ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (x^2 - z0*z1 + z1) * dx +(x^2 - z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-x^2*z0*z1 - x^2*z1 - z0^2*z1 + z0*z1 - z1)/x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-z0^2*z1^2 + z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (x^2*z0 + z0^2*z1 + z1^2) * dx +(x^2*z0 + z0^2*z1 + z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-x^4*z0^2 + x^4*z0 + x^4*z1 - x^4 + z1^2)/x^3) * dx, z1^2/x^2 ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (x*z0 - x) * dx +(x*z0 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((x^2*z1^2 + z0*z1^2 + z1^2)/x^3) * dx, (z0*z1^2 + z1^2)/x^2 ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (x*z0^2 - x*z1) * dx +(x*z0^2 - x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((x^4*z0^2 - x^4*z0 - x^2*z0*z1^2 + x^4 - x^2*z1^2 + z0^2*z1^2 - z0*z1^2 + z1^2)/x^3) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (x*z0^2 - x*z0 - x*z1 + x) * dx +(x*z0^2 - x*z0 - x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) +? (x^2*z1 - z0*z1^2 + z1^2)/x^3 +(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2 +if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True +hol_form ((-x^4 - z1^2 - z1)/x^2) * dx +((-x^4 - z1^2 - z1)/x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [5], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :80, in coordinates(self, threshold, basis) + +File :85, in coordinates(self, basis) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_() + 786 return self._call_with_args(x, args, kwds) + 787 +--> 788 cpdef Element _call_(self, x): + 789 """ + 790 Call method with a single argument, not implemented in the base class. + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check) + 1249 return num + 1250 if check and not den.is_unit(): + 1251 # This should probably be a ValueError. + 1252 # However, too much existing code is expecting this to throw a + 1253 # TypeError, so we decided to keep it for the time being. +-> 1254 raise TypeError("fraction must have unit denominator") + 1255 return num * den.inverse_of_unit() + +TypeError: fraction must have unit denominator +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.serre_duality_pairing(f)[?7h[?12l[?25h[?25l[?7lf = AS.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7lom = AS.holomorphic_differentials_basis()[1][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom = AS.holomorphic_differentials_basis()[1][?7h[?12l[?25h[?25l[?7lsage: om = AS.holomorphic_differentials_basis()[1] +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = AS.holomorphic_differentials_basis()[1][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.serre_duality_pairing(f)[?7h[?12l[?25h[?25l[?7lf = AS.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7lsage: f = AS.cohomology_of_structure_sheaf_basis()[1] +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = AS.holomorphic_differentials_basis()[1][?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.serre_duality_pairng(f)[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lerre_duality_pairing(f)[?7h[?12l[?25h[?25l[?7lsage: om.serre_duality_pairing(f) +[?7h[?12l[?25h[?2004l[?7h0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = AS.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7lori, j in enumerate(lll):[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lmology_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 f in AS.cohomology_of_structure_sheaf_basis(): +....: [?7h[?12l[?25h[?25l[?7lprint(i, j)[?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[?7l.[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lrre_duality_pairing[?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....:  print(om.serre_duality_pairing(f)) +....: [?7h[?12l[?25h[?25l[?7lsage: for f in AS.cohomology_of_structure_sheaf_basis(): +....:  print(om.serre_duality_pairing(f)) +....:  +[?7h[?12l[?25h[?2004l0 +0 +0 +0 +2 +0 +0 +0 +0 +0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor f in AS.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lf in AS.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7lsage: for f in AS.cohomology_of_structure_sheaf_basis(): +....: [?7h[?12l[?25h[?25l[?7lfor b in [3, 5, 7, 13, 23, 67, 89, 397, 683, 2113]:[?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[?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[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lmorphic_differentials_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7l....:  for omega in AS.holomorphic_differentials_basis(): +....: [?7h[?12l[?25h[?25l[?7lprint(a)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_duality_pairing[?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....:  print(om.serre_duality_pairing(f)) +....: [?7h[?12l[?25h[?25l[?7lsage: for f in AS.cohomology_of_structure_sheaf_basis(): +....:  for omega in AS.holomorphic_differentials_basis(): +....:  print(om.serre_duality_pairing(f)) +....:  +[?7h[?12l[?25h[?2004l0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +2 +2 +2 +2 +2 +2 +2 +2 +2 +2 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for f in AS.cohomology_of_structure_sheaf_basis(): +....:  for omega in AS.holomorphic_differentials_basis(): +....:  print(om.serre_duality_pairing(f))[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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 in AS.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7li,f in AS.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7l f in AS.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leAS.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7lnAS.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7luAS.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7lmAS.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7leAS.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7lrAS.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7laAS.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7ltAS.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7leAS.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7lenumerate(AS.cohomology_of_structure_sheaf_basis():[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l +[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()):[?7h[?12l[?25h[?25l[?7l() +[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ljomega in AS.holomorphic_diferentials_basis():[?7h[?12l[?25h[?25l[?7l,omega in AS.holomorphic_diferentials_basis():[?7h[?12l[?25h[?25l[?7l omega in AS.holomorphic_diferentials_basis():[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leAS.holomorphic_diferentials_basis():[?7h[?12l[?25h[?25l[?7lnAS.holomorphic_diferentials_basis():[?7h[?12l[?25h[?25l[?7luAS.holomorphic_diferentials_basis():[?7h[?12l[?25h[?25l[?7lmAS.holomorphic_diferentials_basis():[?7h[?12l[?25h[?25l[?7leAS.holomorphic_diferentials_basis():[?7h[?12l[?25h[?25l[?7lrAS.holomorphic_diferentials_basis():[?7h[?12l[?25h[?25l[?7laAS.holomorphic_diferentials_basis():[?7h[?12l[?25h[?25l[?7ltAS.holomorphic_diferentials_basis():[?7h[?12l[?25h[?25l[?7leAS.holomorphic_diferentials_basis():[?7h[?12l[?25h[?25l[?7lenumerate(AS.holomorphic_diferentials_basis():[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l +()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()):[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l +()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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(om.sere_duality_pairing(f))[?7h[?12l[?25h[?25l[?7l(om.sere_duality_pairing(f))[?7h[?12l[?25h[?25l[?7l(om.sere_duality_pairing(f))[?7h[?12l[?25h[?25l[?7l(om.sere_duality_pairing(f))[?7h[?12l[?25h[?25l[?7l(om.sere_duality_pairing(f))[?7h[?12l[?25h[?25l[?7li(om.sere_duality_pairing(f))[?7h[?12l[?25h[?25l[?7lif(om.sere_duality_pairing(f))[?7h[?12l[?25h[?25l[?7l (om.sere_duality_pairing(f))[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?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[?7l0[?7h[?12l[?25h[?25l[?7lL[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l....:  if (om.serre_duality_pairing(f)) != 0: +....: [?7h[?12l[?25h[?25l[?7lprint("Collision")[?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[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lj[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l....:  print(i, j) +....: [?7h[?12l[?25h[?25l[?7lsage: for i, f in enumerate(AS.cohomology_of_structure_sheaf_basis()): +....:  for j, omega in enumerate(AS.holomorphic_differentials_basis()): +....:  if (om.serre_duality_pairing(f)) != 0: +....:  print(i, j) +....:  +[?7h[?12l[?25h[?2004l4 0 +4 1 +4 2 +4 3 +4 4 +4 5 +4 6 +4 7 +4 8 +4 9 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +(0, 0, 2, 0, 0, 0, 0, 0, 0, 0) +(0, 0, 0, 0, 0, 2, 0, 0, 0, 0) +(0, 0, 0, 0, 2, 0, 0, 0, 0, 0) +(0, 0, 0, 2, 0, 0, 0, 0, 0, 0) +(0, 2, 2, 0, 0, 0, 0, 0, 0, 0) +(2, 0, 2, 0, 0, 2, 0, 0, 0, 0) +(0, 0, 0, 0, 0, 0, 0, 1, 0, 0) +(0, 0, 0, 0, 0, 0, 0, 0, 2, 0) +(0, 0, 0, 0, 0, 0, 2, 1, 0, 0) +(0, 0, 0, 0, 0, 0, 0, 0, 0, 2) +(0, 0, 2, 0, 0, 0, 0, 0, 0, 0) +(0, 0, 0, 0, 0, 2, 0, 0, 0, 0) +(0, 0, 0, 0, 2, 0, 0, 0, 0, 0) +(0, 0, 0, 2, 0, 0, 0, 0, 0, 0) +(0, 2, 2, 0, 0, 0, 0, 0, 0, 0) +(2, 0, 2, 0, 0, 2, 0, 0, 0, 0) +(0, 0, 0, 0, 0, 0, 0, 1, 0, 0) +(0, 0, 0, 0, 0, 0, 0, 0, 2, 0) +(0, 0, 0, 0, 0, 0, 2, 1, 0, 0) +(0, 0, 0, 0, 0, 0, 0, 0, 0, 2) +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +nowe!!!! ( (1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (1) * dx +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (z1) * dx +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0 + 1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (z0 + 1) * dx +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0*z1 + z1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (z0*z1 + z1) * dx +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0^2 - z0 + 1) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (z0^2 - z0 + 1) * dx +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (x) * dx +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x*z0 + x) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (x*z0 + x) * dx +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2) * dx, 0 ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-x^4 - z1)/x^2) * dx, z1/x ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-z1^2)/x^2) * dx, z1^2/x ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((x^2*z1 - z0*z1 - z1)/x^2) * dx, (z0*z1 + z1)/x ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((x^4*z0 + x^2*z0^2*z1 + x^4 - x^2*z0*z1 + x^2*z1^2 + x^2*z1 - z0*z1^2 - z1^2)/x^2) * dx, (z0*z1^2 + z1^2)/x ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (x^2 - z0*z1 + z1) * dx +(x^2 - z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-x^2*z0*z1 - x^2*z1 - z0^2*z1 + z0*z1 - z1)/x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-z0^2*z1^2 + z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (x^2*z0 + z0^2*z1 + z1^2) * dx +(x^2*z0 + z0^2*z1 + z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-x^4*z0^2 + x^4*z0 + x^4*z1 - x^4 + z1^2)/x^3) * dx, z1^2/x^2 ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (x*z0 - x) * dx +(x*z0 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((x^2*z1^2 + z0*z1^2 + z1^2)/x^3) * dx, (z0*z1^2 + z1^2)/x^2 ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (x*z0^2 - x*z1) * dx +(x*z0^2 - x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((x^4*z0^2 - x^4*z0 - x^2*z0*z1^2 + x^4 - x^2*z1^2 + z0^2*z1^2 - z0*z1^2 + z1^2)/x^3) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) +? 0 +0 q r: 0 0 +if 0 True +hol_form (x*z0^2 - x*z0 - x*z1 + x) * dx +(x*z0^2 - x*z0 - x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) +? (x^2*z1 - z0*z1^2 + z1^2)/x^3 +(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2 +if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True +hol_form ((-x^4 - z1^2 - z1)/x^2) * dx +((-x^4 - z1^2 - z1)/x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [12], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :80, in coordinates(self, threshold, basis) + +File :85, in coordinates(self, basis) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_() + 786 return self._call_with_args(x, args, kwds) + 787 +--> 788 cpdef Element _call_(self, x): + 789 """ + 790 Call method with a single argument, not implemented in the base class. + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check) + 1249 return num + 1250 if check and not den.is_unit(): + 1251 # This should probably be a ValueError. + 1252 # However, too much existing code is expecting this to throw a + 1253 # TypeError, so we decided to keep it for the time being. +-> 1254 raise TypeError("fraction must have unit denominator") + 1255 return num * den.inverse_of_unit() + +TypeError: fraction must have unit denominator +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: for i, f in enumerate(AS.cohomology_of_structure_sheaf_basis()): +....:  for j, omega in enumerate(AS.holomorphic_differentials_basis()): +....:  if (om.serre_duality_pairing(f)) != 0: +....:  print(i, j)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l +()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l +[?7h[?12l[?25h[?25l[?7l +()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?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, j) +....: [?7h[?12l[?25h[?25l[?7lsage: for i, f in enumerate(AS.cohomology_of_structure_sheaf_basis()): +....:  for j, omega in enumerate(AS.holomorphic_differentials_basis()): +....:  if (om.serre_duality_pairing(f)) != 0: +....:  print(i, j) +....:  +[?7h[?12l[?25h[?2004l(0, 0, 2, 0, 0, 0, 0, 0, 0, 0) +(0, 0, 0, 0, 0, 2, 0, 0, 0, 0) +(0, 0, 0, 0, 2, 0, 0, 0, 0, 0) +(0, 0, 0, 2, 0, 0, 0, 0, 0, 0) +(0, 2, 2, 0, 0, 0, 0, 0, 0, 0) +(2, 0, 2, 0, 0, 2, 0, 0, 0, 0) +(0, 0, 0, 0, 0, 0, 0, 1, 0, 0) +(0, 0, 0, 0, 0, 0, 0, 0, 2, 0) +(0, 0, 0, 0, 0, 0, 2, 1, 0, 0) +(0, 0, 0, 0, 0, 0, 0, 0, 0, 2) +--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Input In [13], in () + 1 for i, f in enumerate(AS.cohomology_of_structure_sheaf_basis()): + 2 for j, omega in enumerate(AS.holomorphic_differentials_basis()): +----> 3 if (om.serre_duality_pairing(f)) != Integer(0): + 4 print(i, j) + +File :117, in serre_duality_pairing(self, fct) + +File /ext/sage/9.7/src/sage/misc/functional.py:585, in symbolic_sum(expression, *args, **kwds) + 583 return expression.sum(*args, **kwds) + 584 elif max(len(args),len(kwds)) <= 1: +--> 585 return sum(expression, *args, **kwds) + 586 else: + 587 from sage.symbolic.ring import SR + +File :117, in (.0) + +AttributeError: 'NoneType' object has no attribute 'residue' +[?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[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lcohlogy_of_structure_hef_basis()[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lmology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.cohomology_of_structure_sheaf_basis() +[?7h[?12l[?25h[?2004l(0, 0, 2, 0, 0, 0, 0, 0, 0, 0) +(0, 0, 0, 0, 0, 2, 0, 0, 0, 0) +(0, 0, 0, 0, 2, 0, 0, 0, 0, 0) +(0, 0, 0, 2, 0, 0, 0, 0, 0, 0) +(0, 2, 2, 0, 0, 0, 0, 0, 0, 0) +(2, 0, 2, 0, 0, 2, 0, 0, 0, 0) +(0, 0, 0, 0, 0, 0, 0, 1, 0, 0) +(0, 0, 0, 0, 0, 0, 0, 0, 2, 0) +(0, 0, 0, 0, 0, 0, 2, 1, 0, 0) +(0, 0, 0, 0, 0, 0, 0, 0, 0, 2) +[?7h[z1/x, + z1^2/x, + z0*z1/x, + z0*z1^2/x, + z0^2*z1/x, + z0^2*z1^2/x, + z1^2/x^2, + z0*z1^2/x^2, + z0^2*z1^2/x^2, + z0^2*z1^2/x^3] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: AS.cohomology_of_structure_sheaf_basis()[1] +[?7h[?12l[?25h[?2004l(0, 0, 2, 0, 0, 0, 0, 0, 0, 0) +(0, 0, 0, 0, 0, 2, 0, 0, 0, 0) +(0, 0, 0, 0, 2, 0, 0, 0, 0, 0) +(0, 0, 0, 2, 0, 0, 0, 0, 0, 0) +(0, 2, 2, 0, 0, 0, 0, 0, 0, 0) +(2, 0, 2, 0, 0, 2, 0, 0, 0, 0) +(0, 0, 0, 0, 0, 0, 0, 1, 0, 0) +(0, 0, 0, 0, 0, 0, 0, 0, 2, 0) +(0, 0, 0, 0, 0, 0, 2, 1, 0, 0) +(0, 0, 0, 0, 0, 0, 0, 0, 0, 2) +[?7hz1^2/x +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7l AS.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7l=AS.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7l AS.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?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 = AS.cohomology_of_structure_sheaf_basis()[1] +[?7h[?12l[?25h[?2004l(0, 0, 2, 0, 0, 0, 0, 0, 0, 0) +(0, 0, 0, 0, 0, 2, 0, 0, 0, 0) +(0, 0, 0, 0, 2, 0, 0, 0, 0, 0) +(0, 0, 0, 2, 0, 0, 0, 0, 0, 0) +(0, 2, 2, 0, 0, 0, 0, 0, 0, 0) +(2, 0, 2, 0, 0, 2, 0, 0, 0, 0) +(0, 0, 0, 0, 0, 0, 0, 1, 0, 0) +(0, 0, 0, 0, 0, 0, 0, 0, 2, 0) +(0, 0, 0, 0, 0, 0, 2, 1, 0, 0) +(0, 0, 0, 0, 0, 0, 0, 0, 0, 2) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.serre_duality_pairing(f)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = AS.holomorphic_dfferentials_basis()[1][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[1][?7h[?12l[?25h[?25l[?7lsage: om = AS.holomorphic_differentials_basis()[1] +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = AS.holomorphic_differentials_basis()[1][?7h[?12l[?25h[?25l[?7lm.serre_duality_pairng(f)[?7h[?12l[?25h[?25l[?7lserre_duality_pairing(f)[?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[?7lsage: om.serre_duality_pairing(A) +[?7h[?12l[?25h[?2004l[?7h0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.serre_duality_pairing(A)[?7h[?12l[?25h[?25l[?7l = AS.holomorphic_dfferentials_basis()[1][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l2][?7h[?12l[?25h[?25l[?7lsage: om = AS.holomorphic_differentials_basis()[2] +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = AS.holomorphic_differentials_basis()[2][?7h[?12l[?25h[?25l[?7l.serre_duality_pairng(A)[?7h[?12l[?25h[?25l[?7lsage: om.serre_duality_pairing(A) +[?7h[?12l[?25h[?2004l[?7h0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.serre_duality_pairing(A)[?7h[?12l[?25h[?25l[?7l = AS.holomorphic_dfferentials_basis()[2][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l3][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7lsage: om = AS.holomorphic_differentials_basis()[3] +[?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[?7lom = AS.holomorphic_differentials_basis()[3][?7h[?12l[?25h[?25l[?7l.serre_duality_pairng(A)[?7h[?12l[?25h[?25l[?7lsage: om.serre_duality_pairing(A) +[?7h[?12l[?25h[?2004l[?7h0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.serre_duality_pairing(A)[?7h[?12l[?25h[?25l[?7l = AS.holomorphic_dfferentials_basis()[3][?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[?7ls[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lduality_pairing[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om = AS.holomorphic_differentials_basis()[3]; om.serre_duality_pairing(A) +[?7h[?12l[?25h[?2004l[?7h0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = AS.holomorphic_differentials_basis()[3]; om.serre_duality_pairing(A)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l]; om.sere_duality_pairing(A)[?7h[?12l[?25h[?25l[?7l4]; om.sere_duality_pairing(A)[?7h[?12l[?25h[?25l[?7lsage: om = AS.holomorphic_differentials_basis()[4]; om.serre_duality_pairing(A) +[?7h[?12l[?25h[?2004l[?7h0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = AS.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7lS.cohomlgy_f_strucure_shaf_bsis()[1][?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lhlrphic_differential_bsis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llomorphic_differentials_basis()[?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[(1) * dx, + (z1) * dx, + (x^2*z0 + z0^2*z1 + z1^2) * dx, + (z0) * dx, + (z0*z1) * dx, + (z0^2) * dx, + (x) * dx, + (-x*z0^2 + x*z1) * dx, + (x*z0) * dx, + (x^2) * dx] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lom = AS.holomorphic_differentils_basis()[4]; om.serre_duality_pairing(A)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l]; om.sere_duality_pairing(A)[?7h[?12l[?25h[?25l[?7l5]; om.sere_duality_pairing(A)[?7h[?12l[?25h[?25l[?7lsage: om = AS.holomorphic_differentials_basis()[5]; om.serre_duality_pairing(A) +[?7h[?12l[?25h[?2004l[?7h2 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = AS.holomorphic_differentials_basis()[5]; om.serre_duality_pairing(A)[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_bsis()[?7h[?12l[?25h[?25l[?7lom = AS.holomorphic_differentils_basis()[4]; om.serre_duality_pairing(A)[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l.serre_duality_pairng(A)[?7h[?12l[?25h[?25l[?7l = AS.holomorphic_dfferentials_basis()[3][?7h[?12l[?25h[?25l[?7l.serre_duality_pairng(A)[?7h[?12l[?25h[?25l[?7l = AS.holomorphic_dfferentials_basis()[2][?7h[?12l[?25h[?25l[?7l.serre_duality_pairng(A)[?7h[?12l[?25h[?25l[?7l = AS.holomorphic_dfferentials_basis()[1][?7h[?12l[?25h[?25l[?7lA = AS.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7lS.cohomlgy_f_strucure_shaf_bsis()[1][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: for i, f in enumerate(AS.cohomology_of_structure_sheaf_basis()): +....:  for j, omega in enumerate(AS.holomorphic_differentials_basis()): +....:  if (om.serre_duality_pairing(f)) != 0: +....:  print(i, j)[?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[?7lfor i, f in enumerate(AS.cohomology_of_structure_sheaf_basis()): +....:  for j, omega in enumerate(AS.holomorphic_differentials_basis()): +....:  if (om.serre_duality_pairing(f)) != 0: +....:  print(i, j)[?7h[?12l[?25h[?25l[?7lload('init.sage') +  +  + [?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lTraceback (most recent call last): + + File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code + exec(code_obj, self.user_global_ns, self.user_ns) + + Input In [27] in  + load('init.sage') + + File sage/misc/persist.pyx:175 in sage.misc.persist.load + sage.repl.load.load(filename, globals()) + + File /ext/sage/9.7/src/sage/repl/load.py:272 in load + exec(preparse_file(f.read()) + "\n", globals) + + File :8 in  + + File sage/misc/persist.pyx:175 in sage.misc.persist.load + sage.repl.load.load(filename, globals()) + + File /ext/sage/9.7/src/sage/repl/load.py:272 in load + exec(preparse_file(f.read()) + "\n", globals) + + File :68 + print('products:' [omega.serre_duality_pairing(self.f) for omega in AS.holomorphic_differentials_basis()]) + ^ +SyntaxError: invalid syntax. Perhaps you forgot a comma? + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +nowe!!!! ( (1) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (1) * dx +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z1) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (z1) * dx +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0 + 1) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (z0 + 1) * dx +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0*z1 + z1) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (z0*z1 + z1) * dx +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0^2 - z0 + 1) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (z0^2 - z0 + 1) * dx +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (x) * dx +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x*z0 + x) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (x*z0 + x) * dx +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-x^4 - z1)/x^2) * dx, z1/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-z1^2)/x^2) * dx, z1^2/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((x^2*z1 - z0*z1 - z1)/x^2) * dx, (z0*z1 + z1)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((x^4*z0 + x^2*z0^2*z1 + x^4 - x^2*z0*z1 + x^2*z1^2 + x^2*z1 - z0*z1^2 - z1^2)/x^2) * dx, (z0*z1^2 + z1^2)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (x^2 - z0*z1 + z1) * dx +(x^2 - z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-x^2*z0*z1 - x^2*z1 - z0^2*z1 + z0*z1 - z1)/x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-z0^2*z1^2 + z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (x^2*z0 + z0^2*z1 + z1^2) * dx +(x^2*z0 + z0^2*z1 + z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-x^4*z0^2 + x^4*z0 + x^4*z1 - x^4 + z1^2)/x^3) * dx, z1^2/x^2 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (x*z0 - x) * dx +(x*z0 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((x^2*z1^2 + z0*z1^2 + z1^2)/x^3) * dx, (z0*z1^2 + z1^2)/x^2 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (x*z0^2 - x*z1) * dx +(x*z0^2 - x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((x^4*z0^2 - x^4*z0 - x^2*z0*z1^2 + x^4 - x^2*z1^2 + z0^2*z1^2 - z0*z1^2 + z1^2)/x^3) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (x*z0^2 - x*z0 - x*z1 + x) * dx +(x*z0^2 - x*z0 - x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( ((-z0*z1^2 - z1^2)/x^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? (x^2*z1 - z0*z1^2 + z1^2)/x^3 +(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2 +if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True +hol_form ((-x^4 - z1^2 - z1)/x^2) * dx +((-x^4 - z1^2 - z1)/x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [28], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :81, in coordinates(self, threshold, basis) + +File :85, in coordinates(self, basis) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_() + 786 return self._call_with_args(x, args, kwds) + 787 +--> 788 cpdef Element _call_(self, x): + 789 """ + 790 Call method with a single argument, not implemented in the base class. + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check) + 1249 return num + 1250 if check and not den.is_unit(): + 1251 # This should probably be a ValueError. + 1252 # However, too much existing code is expecting this to throw a + 1253 # TypeError, so we decided to keep it for the time being. +-> 1254 raise TypeError("fraction must have unit denominator") + 1255 return num * den.inverse_of_unit() + +TypeError: fraction must have unit denominator +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldR = AS.de_rham_basis(threshold = 20)[?7h[?12l[?25h[?25l[?7le_rham_coodinate(AS, dR[0])[?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[?7lbasis(AS)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lis(AS)[?7h[?12l[?25h[?25l[?7lsage: de_rham_basis(AS) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Input In [29], in () +----> 1 de_rham_basis(AS) + +NameError: name 'de_rham_basis' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_basis(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[?7lAde_rham_basis()[?7h[?12l[?25h[?25l[?7lSde_rham_basis()[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS.de_rham_basis() +[?7h[?12l[?25h[?2004lz1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +[?7h[( (1) * dx, 0 ), + ( (z1) * dx, 0 ), + ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 ), + ( (z0) * dx, 0 ), + ( (z0*z1) * dx, 0 ), + ( (z0^2) * dx, 0 ), + ( (x) * dx, 0 ), + ( (-x*z0^2 + x*z1) * dx, 0 ), + ( (x*z0) * dx, 0 ), + ( (x^2) * dx, 0 ), + ( ((-x^4 - z1)/x^2) * dx, z1/x ), + ( ((-z1^2)/x^2) * dx, z1^2/x ), + ( ((x^2*z1 - z0*z1)/x^2) * dx, z0*z1/x ), + ( ((x^4*z0 + x^2*z0^2*z1 + x^2*z1^2 - z0*z1^2)/x^2) * dx, z0*z1^2/x ), + ( ((-x^2*z0*z1 - z0^2*z1)/x^2) * dx, z0^2*z1/x ), + ( ((-z0^2*z1^2)/x^2) * dx, z0^2*z1^2/x ), + ( ((-x^4*z0^2 + x^4*z1 + z1^2)/x^3) * dx, z1^2/x^2 ), + ( ((x^2*z1^2 + z0*z1^2)/x^3) * dx, z0*z1^2/x^2 ), + ( ((x^4*z0^2 - x^2*z0*z1^2 + z0^2*z1^2)/x^3) * dx, z0^2*z1^2/x^2 ), + ( ((-z0*z1^2)/x^2) * dx, z0^2*z1^2/x^3 )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lgnus()[?7h[?12l[?25h[?25l[?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[?7h10 +[?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(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +nowe!!!! ( (1) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (1) * dx +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z1) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (z1) * dx +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0 + 1) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (z0 + 1) * dx +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0*z1 + z1) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (z0*z1 + z1) * dx +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0^2 - z0 + 1) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (z0^2 - z0 + 1) * dx +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (x) * dx +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x*z0 + x) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (x*z0 + x) * dx +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (0) * dx, z1/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x^2*z1) * dx, z1^2/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2*z0 + x^2) * dx, (z0*z1 + z1)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x^2*z0*z1 + x^2*z0 - x^2*z1 + z0^2*z1 + x^2 - z0*z1 + z1) * dx, (z0*z1^2 + z1^2)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (x^2 - z0*z1 + z1) * dx +(x^2 - z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2*z0^2 - x^2*z0 + x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x^2*z0^2*z1 + x^2*z0*z1 - x^2*z1 + z0*z1^2 + z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (x^2*z0 + z0^2*z1 + z1^2) * dx +(x^2*z0 + z0^2*z1 + z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x*z0^2 + x*z0 - x) * dx, z1^2/x^2 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (x*z0 - x) * dx +(x*z0 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x*z0*z1 - x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (x*z0^2 - x*z1) * dx +(x*z0^2 - x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x*z0^2*z1 + x*z0^2 + x*z0*z1 - x*z0 - x*z1 + x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (x*z0^2 - x*z0 - x*z1 + x) * dx +(x*z0^2 - x*z0 - x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-z0^2*z1 + z0*z1 - z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? (x^2*z1 - z0*z1^2 + z1^2)/x^3 +(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2 +if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True +hol_form (z0*z1 - z1) * dx +(z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (1) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (1) * dx +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z1 + 1) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (z1 + 1) * dx +(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx +(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (z0) * dx +(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0*z1 + z0) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (z0*z1 + z0) * dx +(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0^2) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (z0^2) * dx +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (x) * dx +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x*z0^2 + x*z1 + x) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (-x*z0^2 + x*z1 + x) * dx +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x*z0) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (x*z0) * dx +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (0) * dx, (z1 + 1)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 1/x +1/x q r: 0 1 +if 1/x True +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x^2*z1 - x^2) * dx, (z1^2 - z1 + 1)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 1/x +1/x q r: 0 1 +if 1/x True +hol_form (-x^2) * dx +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2*z0) * dx, (z0*z1 + z0)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? z0/x +z0/x q r: 0 z0 +if z0/x True +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x^2*z0*z1 + z0^2*z1 + z0^2) * dx, (z0*z1^2 - z0*z1 + z0)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? z0/x +z0/x q r: 0 z0 +if z0/x True +hol_form (z0^2) * dx +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2*z0^2) * dx, (z0^2*z1 + z0^2)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? (z0^2 - z1)/x +(z0^2 - z1)/x q r: 0 z0^2 - z1 +if (z0^2 - z1)/x True +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x^2*z0^2*z1 - x^2*z0^2 + z0*z1^2 - z0*z1 + z0) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? (z0^2 - z1)/x +(z0^2 - z1)/x q r: 0 z0^2 - z1 +if (z0^2 - z1)/x True +hol_form (-z0*z1 + z0) * dx +(-z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x*z0^2) * dx, (z1^2 - z1 + 1)/x^2 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? (-z1 + 1)/x^2 +(-z1 + 1)/x^2 q r: 0 -z1 + 1 +if (-z1 + 1)/x^2 True +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x*z0*z1 - x*z0) * dx, (z0*z1^2 - z0*z1 + z0)/x^2 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? (-z0*z1 + z0)/x^2 +(-z0*z1 + z0)/x^2 q r: 0 -z0*z1 + z0 +if (-z0*z1 + z0)/x^2 True +hol_form (-x*z0) * dx +(-x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x*z0^2*z1) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x^2 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? (-z0^2*z1 + z0^2 - z1^2)/x^2 +(-z0^2*z1 + z0^2 - z1^2)/x^2 q r: 0 -z0^2*z1 + z0^2 - z1^2 +if (-z0^2*z1 + z0^2 - z1^2)/x^2 False +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Input In [32], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :82, in coordinates(self, threshold, basis) + +ValueError: I arrived at a form (omega, 0), in which omega is not regular on U0. I hoped this wouldn t happen. +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +nowe!!!! ( (1) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (1) * dx +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z1) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (z1) * dx +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0 + 1) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (z0 + 1) * dx +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0*z1 + z1) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (z0*z1 + z1) * dx +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0^2 - z0 + 1) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (z0^2 - z0 + 1) * dx +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (x) * dx +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x*z0 + x) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (x*z0 + x) * dx +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (0) * dx, z1/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x^2*z1) * dx, z1^2/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2*z0 + x^2) * dx, (z0*z1 + z1)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x^2*z0*z1 + x^2*z0 - x^2*z1 + z0^2*z1 + x^2 - z0*z1 + z1) * dx, (z0*z1^2 + z1^2)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (x^2 - z0*z1 + z1) * dx +(x^2 - z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2*z0^2 - x^2*z0 + x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x^2*z0^2*z1 + x^2*z0*z1 - x^2*z1 + z0*z1^2 + z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (x^2*z0 + z0^2*z1 + z1^2) * dx +(x^2*z0 + z0^2*z1 + z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x*z0^2 + x*z0 - x) * dx, z1^2/x^2 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (x*z0 - x) * dx +(x*z0 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x*z0*z1 - x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (x*z0^2 - x*z1) * dx +(x*z0^2 - x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x*z0^2*z1 + x*z0^2 + x*z0*z1 - x*z0 - x*z1 + x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (x*z0^2 - x*z0 - x*z1 + x) * dx +(x*z0^2 - x*z0 - x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-z0^2*z1 + z0*z1 - z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? (x^2*z1 - z0*z1^2 + z1^2)/x^3 +(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2 +if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True +hol_form (z0*z1 - z1) * dx +(z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (1) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (1) * dx +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z1 + 1) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (z1 + 1) * dx +(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx +(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (z0) * dx +(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0*z1 + z0) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (z0*z1 + z0) * dx +(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0^2) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (z0^2) * dx +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (x) * dx +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x*z0^2 + x*z1 + x) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (-x*z0^2 + x*z1 + x) * dx +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x*z0) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (x*z0) * dx +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (0) * dx, (z1 + 1)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 1/x +1/x q r: 0 1 +if 1/x True +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x^2*z1 - x^2) * dx, (z1^2 - z1 + 1)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 1/x +1/x q r: 0 1 +if 1/x True +hol_form (-x^2) * dx +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2*z0) * dx, (z0*z1 + z0)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? z0/x +z0/x q r: 0 z0 +if z0/x True +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x^2*z0*z1 + z0^2*z1 + z0^2) * dx, (z0*z1^2 - z0*z1 + z0)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? z0/x +z0/x q r: 0 z0 +if z0/x True +hol_form (z0^2) * dx +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2*z0^2) * dx, (z0^2*z1 + z0^2)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? (z0^2 - z1)/x +(z0^2 - z1)/x q r: 0 z0^2 - z1 +if (z0^2 - z1)/x True +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x^2*z0^2*z1 - x^2*z0^2 + z0*z1^2 - z0*z1 + z0) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? (z0^2 - z1)/x +(z0^2 - z1)/x q r: 0 z0^2 - z1 +if (z0^2 - z1)/x True +hol_form (-z0*z1 + z0) * dx +(-z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x*z0^2) * dx, (z1^2 - z1 + 1)/x^2 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? (-z1 + 1)/x^2 +(-z1 + 1)/x^2 q r: 0 -z1 + 1 +if (-z1 + 1)/x^2 True +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x*z0*z1 - x*z0) * dx, (z0*z1^2 - z0*z1 + z0)/x^2 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? (-z0*z1 + z0)/x^2 +(-z0*z1 + z0)/x^2 q r: 0 -z0*z1 + z0 +if (-z0*z1 + z0)/x^2 True +hol_form (-x*z0) * dx +(-x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x*z0^2*z1) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x^2 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? (-z0^2*z1 + z0^2 - z1^2)/x^2 +(-z0^2*z1 + z0^2 - z1^2)/x^2 q r: 0 -z0^2*z1 + z0^2 - z1^2 +if (-z0^2*z1 + z0^2 - z1^2)/x^2 False +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Input In [33], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :82, in coordinates(self, threshold, basis) + +ValueError: I arrived at a form (omega, 0), in which omega is not regular on U0. I hoped this wouldn t happen. +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?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[?7lm[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lmorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?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[?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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?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[?7l1].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[?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[?7lsage: AS.holomorphic_differentials_basis()[1].group_action([1, 0]) +[?7h[?12l[?25h[?2004l[?7h(z1) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[1].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[?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[?7lsage: AS.holomorphic_differentials_basis()[1].group_action([0, 1]) +[?7h[?12l[?25h[?2004l[?7h(z1 + 1) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[1].group_action([0, 1])[?7h[?12l[?25h[?25l[?7l10[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +nowe!!!! ( (1) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (1) * dx +hol_form (1) * dx +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z1) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (z1) * dx +hol_form (z1) * dx +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx +hol_form (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0 + 1) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (z0 + 1) * dx +hol_form (z0 + 1) * dx +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0*z1 + z1) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (z0*z1 + z1) * dx +hol_form (z0*z1 + z1) * dx +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0^2 - z0 + 1) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (z0^2 - z0 + 1) * dx +hol_form (z0^2 - z0 + 1) * dx +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (x) * dx +hol_form (x) * dx +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (-x*z0^2 + x*z0 + x*z1 - x) * dx +hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x*z0 + x) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (x*z0 + x) * dx +hol_form (x*z0 + x) * dx +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (x^2) * dx +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (0) * dx, z1/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (0) * dx +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x^2*z1) * dx, z1^2/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (0) * dx +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2*z0 + x^2) * dx, (z0*z1 + z1)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (x^2) * dx +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x^2*z0*z1 + x^2*z0 - x^2*z1 + z0^2*z1 + x^2 - z0*z1 + z1) * dx, (z0*z1^2 + z1^2)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (x^2 - z0*z1 + z1) * dx +hol_form (x^2 - z0*z1 + z1) * dx +(x^2 - z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2*z0^2 - x^2*z0 + x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (x^2) * dx +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x^2*z0^2*z1 + x^2*z0*z1 - x^2*z1 + z0*z1^2 + z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (x^2*z0 + z0^2*z1 + z1^2) * dx +hol_form (x^2*z0 + z0^2*z1 + z1^2) * dx +(x^2*z0 + z0^2*z1 + z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x*z0^2 + x*z0 - x) * dx, z1^2/x^2 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (x*z0 - x) * dx +hol_form (x*z0 - x) * dx +(x*z0 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x*z0*z1 - x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (x*z0^2 - x*z1) * dx +hol_form (x*z0^2 - x*z1) * dx +(x*z0^2 - x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x*z0^2*z1 + x*z0^2 + x*z0*z1 - x*z0 - x*z1 + x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (x*z0^2 - x*z0 - x*z1 + x) * dx +hol_form (x*z0^2 - x*z0 - x*z1 + x) * dx +(x*z0^2 - x*z0 - x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-z0^2*z1 + z0*z1 - z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? (x^2*z1 - z0*z1^2 + z1^2)/x^3 +(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2 +if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True +omega - df ((x^4 - x^2*z0*z1 + x^2*z1 + z1^2 + z1)/x^2) * dx +hol_form (z0*z1 - z1) * dx +(z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (1) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (1) * dx +hol_form (1) * dx +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z1 + 1) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (z1 + 1) * dx +hol_form (z1 + 1) * dx +(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx +hol_form (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx +(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (z0) * dx +hol_form (z0) * dx +(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0*z1 + z0) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (z0*z1 + z0) * dx +hol_form (z0*z1 + z0) * dx +(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0^2) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (z0^2) * dx +hol_form (z0^2) * dx +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (x) * dx +hol_form (x) * dx +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x*z0^2 + x*z1 + x) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (-x*z0^2 + x*z1 + x) * dx +hol_form (-x*z0^2 + x*z1 + x) * dx +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x*z0) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (x*z0) * dx +hol_form (x*z0) * dx +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (x^2) * dx +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (0) * dx, (z1 + 1)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 1/x +1/x q r: 0 1 +if 1/x True +omega - df (1/x^2) * dx +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x^2*z1 - x^2) * dx, (z1^2 - z1 + 1)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 1/x +1/x q r: 0 1 +if 1/x True +omega - df ((-x^4 + 1)/x^2) * dx +hol_form (-x^2) * dx +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2*z0) * dx, (z0*z1 + z0)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? z0/x +z0/x q r: 0 z0 +if z0/x True +omega - df ((-x^2 + z0)/x^2) * dx +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x^2*z0*z1 + z0^2*z1 + z0^2) * dx, (z0*z1^2 - z0*z1 + z0)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? z0/x +z0/x q r: 0 z0 +if z0/x True +omega - df ((x^2*z0^2 - x^2 + z0)/x^2) * dx +hol_form (z0^2) * dx +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2*z0^2) * dx, (z0^2*z1 + z0^2)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? (z0^2 - z1)/x +(z0^2 - z1)/x q r: 0 z0^2 - z1 +if (z0^2 - z1)/x True +omega - df ((-x^4 + x^2*z0 + z0^2 - z1)/x^2) * dx +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x^2*z0^2*z1 - x^2*z0^2 + z0*z1^2 - z0*z1 + z0) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? (z0^2 - z1)/x +(z0^2 - z1)/x q r: 0 z0^2 - z1 +if (z0^2 - z1)/x True +omega - df ((-x^4 - x^2*z0*z1 - x^2*z0 + z0^2 - z1)/x^2) * dx +hol_form (-z0*z1 + z0) * dx +(-z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x*z0^2) * dx, (z1^2 - z1 + 1)/x^2 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? (-z1 + 1)/x^2 +(-z1 + 1)/x^2 q r: 0 -z1 + 1 +if (-z1 + 1)/x^2 True +omega - df ((-x^4 + z1 - 1)/x^3) * dx +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x*z0*z1 - x*z0) * dx, (z0*z1^2 - z0*z1 + z0)/x^2 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? (-z0*z1 + z0)/x^2 +(-z0*z1 + z0)/x^2 q r: 0 -z0*z1 + z0 +if (-z0*z1 + z0)/x^2 True +omega - df ((x^4*z0 + x^2*z1 - x^2 + z0*z1 - z0)/x^3) * dx +hol_form (-x*z0) * dx +(-x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x*z0^2*z1) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x^2 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? (-z0^2*z1 + z0^2 - z1^2)/x^2 +(-z0^2*z1 + z0^2 - z1^2)/x^2 q r: 0 -z0^2*z1 + z0^2 - z1^2 +if (-z0^2*z1 + z0^2 - z1^2)/x^2 False +omega - df ((-x^4*z0^2 + x^4*z1 - x^2*z0*z1 + x^2*z0 + z0^2*z1 - z0^2 + z1^2)/x^3) * dx +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Input In [36], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :83, in coordinates(self, threshold, basis) + +ValueError: I arrived at a form (omega, 0), in which omega is not regular on U0. I hoped this wouldn t happen. +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[1].group_action([0, 1])[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.de_rham_basis() +[?7h[?12l[?25h[?2004lz1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +[?7h[( (1) * dx, 0 ), + ( (z1) * dx, 0 ), + ( (x^2*z0 + z0^2*z1 + z1^2) * dx, 0 ), + ( (z0) * dx, 0 ), + ( (z0*z1) * dx, 0 ), + ( (z0^2) * dx, 0 ), + ( (x) * dx, 0 ), + ( (-x*z0^2 + x*z1) * dx, 0 ), + ( (x*z0) * dx, 0 ), + ( (x^2) * dx, 0 ), + ( (0) * dx, z1/x ), + ( (-x^2*z1) * dx, z1^2/x ), + ( (x^2*z0) * dx, z0*z1/x ), + ( (-x^2*z0*z1 + x^2*z0 + z0^2*z1) * dx, z0*z1^2/x ), + ( (x^2*z0^2) * dx, z0^2*z1/x ), + ( (-x^2*z0^2*z1 + z0*z1^2) * dx, z0^2*z1^2/x ), + ( (-x*z0^2) * dx, z1^2/x^2 ), + ( (-x*z0*z1) * dx, z0*z1^2/x^2 ), + ( (-x*z0^2*z1 + x*z0^2) * dx, z0^2*z1^2/x^2 ), + ( (-z0^2*z1) * dx, z0^2*z1^2/x^3 )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.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[?7lomAS.de_rham_bais()[?7h[?12l[?25h[?25l[?7l,AS.de_rham_basis()[?7h[?12l[?25h[?25l[?7l AS.de_rham_basis()[?7h[?12l[?25h[?25l[?7lfAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7l AS.de_rham_basis()[?7h[?12l[?25h[?25l[?7l=AS.de_rham_basis()[?7h[?12l[?25h[?25l[?7l AS.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[?7l16[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: om, f = AS.de_rham_basis()[16] +[?7h[?12l[?25h[?2004lz1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [38], in () +----> 1 om, f = AS.de_rham_basis()[Integer(16)] + +TypeError: cannot unpack non-iterable as_cech object +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom, f = AS.de_rham_basis()[16][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?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.de_rham_basis()[16][?7h[?12l[?25h[?25l[?7l= AS.de_rham_basis()[16][?7h[?12l[?25h[?25l[?7l= AS.de_rham_basis()[16][?7h[?12l[?25h[?25l[?7l= AS.de_rham_basis()[16][?7h[?12l[?25h[?25l[?7l= AS.de_rham_basis()[16][?7h[?12l[?25h[?25l[?7l= AS.de_rham_basis()[16][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lc= AS.de_rham_basis()[16][?7h[?12l[?25h[?25l[?7lc= AS.de_rham_basis()[16][?7h[?12l[?25h[?25l[?7l = AS.de_rham_basis()[16][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: cc = AS.de_rham_basis()[16] +[?7h[?12l[?25h[?2004lz1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcc = AS.de_rham_basis()[16][?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[0][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7liffn[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: cc[0] - cc[1].diffn() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [40], in () +----> 1 cc[Integer(0)] - cc[Integer(1)].diffn() + +TypeError: 'as_cech' object is not subscriptable +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcc[0] - cc[1].diffn()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lsage: cc +[?7h[?12l[?25h[?2004l[?7h( (-x*z0^2) * dx, z1^2/x^2 ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcc[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?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] - cc[1].diffn()[?7h[?12l[?25h[?25l[?7l = AS.de_rham_basis()[16][?7h[?12l[?25h[?25l[?7l[0] - cc[1].diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[ - c[1].difn()[?7h[?12l[?25h[?25l[?7l - c[1].difn()[?7h[?12l[?25h[?25l[?7l - c[1].difn()[?7h[?12l[?25h[?25l[?7l. - c[1].difn()[?7h[?12l[?25h[?25l[?7lom- cc[1].diffn()[?7h[?12l[?25h[?25l[?7le - c[1].difn()[?7h[?12l[?25h[?25l[?7lg - c[1].difn()[?7h[?12l[?25h[?25l[?7la - c[1].difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[1.difn()[?7h[?12l[?25h[?25l[?7l.difn()[?7h[?12l[?25h[?25l[?7l.difn()[?7h[?12l[?25h[?25l[?7l.difn()[?7h[?12l[?25h[?25l[?7lf.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[?7lsage: cc.omega - cc.f.diffn() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Input In [42], in () +----> 1 cc.omega - cc.f.diffn() + +AttributeError: 'as_cech' object has no attribute 'omega' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcc.omega - cc.f.diffn()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lsage: cc +[?7h[?12l[?25h[?2004l[?7h( (-x*z0^2) * dx, z1^2/x^2 ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcc[?7h[?12l[?25h[?25l[?7l.omega - cc.f.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[?7l0 - c.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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: cc.omega0 - cc.f.diffn() +[?7h[?12l[?25h[?2004l[?7h((-x^4*z0^2 - x^4*z1 - z1^2)/x^3) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcc.omega0 - cc.f.diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(c.omega0 - c.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[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (cc.omega0 - cc.f.diffn()).expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7h2*t^-3 + t + 2*t^9 + t^13 + t^21 + 2*t^25 + t^29 + 2*t^45 + t^49 + 2*t^61 + 2*t^65 + 2*t^69 + t^73 + t^85 + 2*t^93 + t^97 + t^113 + t^121 + t^129 + 2*t^133 + t^137 + t^141 + 2*t^153 + t^157 + 2*t^169 + 2*t^173 + 2*t^177 + t^189 + t^193 + 2*t^201 + 2*t^205 + t^217 + 2*t^221 + 2*t^225 + 2*t^229 + t^237 + t^241 + 2*t^249 + t^265 + 2*t^273 + t^277 + t^289 + 2*t^297 + t^301 + 2*t^309 + t^313 + t^325 + 2*t^333 + t^345 + t^349 + 2*t^353 + t^357 + t^361 + t^365 + t^373 + 2*t^385 + 2*t^389 + t^397 + t^421 + 2*t^433 + t^437 + t^441 + t^445 + t^453 + t^457 + t^461 + t^465 + 2*t^477 + t^481 + 2*t^489 + 2*t^493 + 2*t^501 + 2*t^505 + t^513 + t^517 + 2*t^525 + 2*t^537 + t^541 + 2*t^545 + 2*t^549 + 2*t^561 + t^565 + t^569 + 2*t^573 + t^577 + t^585 + t^589 + 2*t^597 + 2*t^601 + t^609 + t^613 + 2*t^621 + t^625 + 2*t^633 + t^637 + 2*t^645 + 2*t^649 + t^657 + t^661 + 2*t^669 + t^685 + 2*t^689 + 2*t^693 + 2*t^697 + t^705 + t^709 + 2*t^717 + 2*t^721 + t^729 + t^733 + 2*t^741 + 2*t^745 + t^757 + 2*t^765 + 2*t^777 + t^781 + t^785 + 2*t^789 + 2*t^793 + t^805 + 2*t^813 + t^817 + t^829 + 2*t^837 + t^853 + 2*t^861 + t^877 + 2*t^885 + 2*t^897 + t^901 + 2*t^909 + t^913 + t^921 + t^925 + t^929 + 2*t^933 + 2*t^945 + t^949 + 2*t^957 + 2*t^961 + O(t^969) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls.coefficient_matrix()[?7h[?12l[?25h[?25l[?7la[?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(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +omega val 0 +z1^2/x +omega val 12 +z0*z1/x +omega val 6 +z0*z1^2/x +omega val 2 +z0^2*z1/x +omega val 0 +z0^2*z1^2/x +omega val 0 +z1^2/x^2 +omega val 1 +z0*z1^2/x^2 +omega val 3 +z0^2*z1^2/x^2 +omega val 1 +z0^2*z1^2/x^3 +omega val 6 +nowe!!!! ( (1) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (1) * dx +hol_form (1) * dx +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z1) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (z1) * dx +hol_form (z1) * dx +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx +hol_form (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0 + 1) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (z0 + 1) * dx +hol_form (z0 + 1) * dx +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0*z1 + z1) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (z0*z1 + z1) * dx +hol_form (z0*z1 + z1) * dx +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0^2 - z0 + 1) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (z0^2 - z0 + 1) * dx +hol_form (z0^2 - z0 + 1) * dx +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (x) * dx +hol_form (x) * dx +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (-x*z0^2 + x*z0 + x*z1 - x) * dx +hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x*z0 + x) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (x*z0 + x) * dx +hol_form (x*z0 + x) * dx +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (x^2) * dx +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (0) * dx, z1/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (0) * dx +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x^2*z1) * dx, z1^2/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (0) * dx +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2*z0 + x^2) * dx, (z0*z1 + z1)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (x^2) * dx +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x^2*z0*z1 + x^2*z0 - x^2*z1 + z0^2*z1 + x^2 - z0*z1 + z1) * dx, (z0*z1^2 + z1^2)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (x^2 - z0*z1 + z1) * dx +hol_form (x^2 - z0*z1 + z1) * dx +(x^2 - z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2*z0^2 - x^2*z0 + x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (x^2) * dx +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x^2*z0^2*z1 + x^2*z0*z1 - x^2*z1 + z0*z1^2 + z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (x^2*z0 + z0^2*z1 + z1^2) * dx +hol_form (x^2*z0 + z0^2*z1 + z1^2) * dx +(x^2*z0 + z0^2*z1 + z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x*z0^2 + x*z0 - x) * dx, z1^2/x^2 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (x*z0 - x) * dx +hol_form (x*z0 - x) * dx +(x*z0 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x*z0*z1 - x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (x*z0^2 - x*z1) * dx +hol_form (x*z0^2 - x*z1) * dx +(x*z0^2 - x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x*z0^2*z1 + x*z0^2 + x*z0*z1 - x*z0 - x*z1 + x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (x*z0^2 - x*z0 - x*z1 + x) * dx +hol_form (x*z0^2 - x*z0 - x*z1 + x) * dx +(x*z0^2 - x*z0 - x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-z0^2*z1 + z0*z1 - z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? (x^2*z1 - z0*z1^2 + z1^2)/x^3 +(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2 +if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True +omega - df ((x^4 - x^2*z0*z1 + x^2*z1 + z1^2 + z1)/x^2) * dx +hol_form (z0*z1 - z1) * dx +(z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (1) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (1) * dx +hol_form (1) * dx +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z1 + 1) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (z1 + 1) * dx +hol_form (z1 + 1) * dx +(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx +hol_form (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx +(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (z0) * dx +hol_form (z0) * dx +(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0*z1 + z0) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (z0*z1 + z0) * dx +hol_form (z0*z1 + z0) * dx +(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0^2) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (z0^2) * dx +hol_form (z0^2) * dx +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (x) * dx +hol_form (x) * dx +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x*z0^2 + x*z1 + x) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (-x*z0^2 + x*z1 + x) * dx +hol_form (-x*z0^2 + x*z1 + x) * dx +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x*z0) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (x*z0) * dx +hol_form (x*z0) * dx +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (x^2) * dx +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (0) * dx, (z1 + 1)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 1/x +1/x q r: 0 1 +if 1/x True +omega - df (1/x^2) * dx +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x^2*z1 - x^2) * dx, (z1^2 - z1 + 1)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 1/x +1/x q r: 0 1 +if 1/x True +omega - df ((-x^4 + 1)/x^2) * dx +hol_form (-x^2) * dx +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2*z0) * dx, (z0*z1 + z0)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? z0/x +z0/x q r: 0 z0 +if z0/x True +omega - df ((-x^2 + z0)/x^2) * dx +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x^2*z0*z1 + z0^2*z1 + z0^2) * dx, (z0*z1^2 - z0*z1 + z0)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? z0/x +z0/x q r: 0 z0 +if z0/x True +omega - df ((x^2*z0^2 - x^2 + z0)/x^2) * dx +hol_form (z0^2) * dx +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2*z0^2) * dx, (z0^2*z1 + z0^2)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? (z0^2 - z1)/x +(z0^2 - z1)/x q r: 0 z0^2 - z1 +if (z0^2 - z1)/x True +omega - df ((-x^4 + x^2*z0 + z0^2 - z1)/x^2) * dx +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x^2*z0^2*z1 - x^2*z0^2 + z0*z1^2 - z0*z1 + z0) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? (z0^2 - z1)/x +(z0^2 - z1)/x q r: 0 z0^2 - z1 +if (z0^2 - z1)/x True +omega - df ((-x^4 - x^2*z0*z1 - x^2*z0 + z0^2 - z1)/x^2) * dx +hol_form (-z0*z1 + z0) * dx +(-z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x*z0^2) * dx, (z1^2 - z1 + 1)/x^2 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? (-z1 + 1)/x^2 +(-z1 + 1)/x^2 q r: 0 -z1 + 1 +if (-z1 + 1)/x^2 True +omega - df ((-x^4 + z1 - 1)/x^3) * dx +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x*z0*z1 - x*z0) * dx, (z0*z1^2 - z0*z1 + z0)/x^2 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? (-z0*z1 + z0)/x^2 +(-z0*z1 + z0)/x^2 q r: 0 -z0*z1 + z0 +if (-z0*z1 + z0)/x^2 True +omega - df ((x^4*z0 + x^2*z1 - x^2 + z0*z1 - z0)/x^3) * dx +hol_form (-x*z0) * dx +(-x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x*z0^2*z1) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x^2 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? (-z0^2*z1 + z0^2 - z1^2)/x^2 +(-z0^2*z1 + z0^2 - z1^2)/x^2 q r: 0 -z0^2*z1 + z0^2 - z1^2 +if (-z0^2*z1 + z0^2 - z1^2)/x^2 False +omega - df ((-x^4*z0^2 + x^4*z1 - x^2*z0*z1 + x^2*z0 + z0^2*z1 - z0^2 + z1^2)/x^3) * dx +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Input In [46], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :84, in coordinates(self, threshold, basis) + +ValueError: I arrived at a form (omega, 0), in which omega is not regular on U0. I hoped this wouldn t happen. +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l,[?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[?7h10 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(cc.omega0 - cc.f.diffn()).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +11 10 +omega val 0 +z1^2/x +11 10 +omega val 12 +z0*z1/x +11 10 +omega val 6 +z0*z1^2/x +11 10 +omega val 2 +z0^2*z1/x +11 10 +omega val 0 +z0^2*z1^2/x +11 10 +omega val 0 +z1^2/x^2 +11 10 +omega val 1 +z0*z1^2/x^2 +11 10 +omega val 3 +z0^2*z1^2/x^2 +11 10 +omega val 1 +z0^2*z1^2/x^3 +11 10 +omega val 6 +nowe!!!! ( (1) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (1) * dx +hol_form (1) * dx +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z1) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (z1) * dx +hol_form (z1) * dx +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx +hol_form (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0 + 1) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (z0 + 1) * dx +hol_form (z0 + 1) * dx +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0*z1 + z1) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (z0*z1 + z1) * dx +hol_form (z0*z1 + z1) * dx +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0^2 - z0 + 1) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (z0^2 - z0 + 1) * dx +hol_form (z0^2 - z0 + 1) * dx +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (x) * dx +hol_form (x) * dx +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (-x*z0^2 + x*z0 + x*z1 - x) * dx +hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x*z0 + x) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (x*z0 + x) * dx +hol_form (x*z0 + x) * dx +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (x^2) * dx +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (0) * dx, z1/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (0) * dx +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x^2*z1) * dx, z1^2/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (0) * dx +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2*z0 + x^2) * dx, (z0*z1 + z1)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (x^2) * dx +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x^2*z0*z1 + x^2*z0 - x^2*z1 + z0^2*z1 + x^2 - z0*z1 + z1) * dx, (z0*z1^2 + z1^2)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (x^2 - z0*z1 + z1) * dx +hol_form (x^2 - z0*z1 + z1) * dx +(x^2 - z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2*z0^2 - x^2*z0 + x^2) * dx, (z0^2*z1 - z0*z1 + z1)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (x^2) * dx +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x^2*z0^2*z1 + x^2*z0*z1 - x^2*z1 + z0*z1^2 + z1^2) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (x^2*z0 + z0^2*z1 + z1^2) * dx +hol_form (x^2*z0 + z0^2*z1 + z1^2) * dx +(x^2*z0 + z0^2*z1 + z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x*z0^2 + x*z0 - x) * dx, z1^2/x^2 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (x*z0 - x) * dx +hol_form (x*z0 - x) * dx +(x*z0 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x*z0*z1 - x*z1) * dx, (z0*z1^2 + z1^2)/x^2 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (x*z0^2 - x*z1) * dx +hol_form (x*z0^2 - x*z1) * dx +(x*z0^2 - x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x*z0^2*z1 + x*z0^2 + x*z0*z1 - x*z0 - x*z1 + x) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^2 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (x*z0^2 - x*z0 - x*z1 + x) * dx +hol_form (x*z0^2 - x*z0 - x*z1 + x) * dx +(x*z0^2 - x*z0 - x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-z0^2*z1 + z0*z1 - z1) * dx, (z0^2*z1^2 - z0*z1^2 + z1^2)/x^3 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? (x^2*z1 - z0*z1^2 + z1^2)/x^3 +(x^2*z1 - z0*z1^2 + z1^2)/x^3 q r: 0 x^2*z1 - z0*z1^2 + z1^2 +if (x^2*z1 - z0*z1^2 + z1^2)/x^3 True +omega - df ((x^4 - x^2*z0*z1 + x^2*z1 + z1^2 + z1)/x^2) * dx +hol_form (z0*z1 - z1) * dx +(z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (1) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (1) * dx +hol_form (1) * dx +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z1 + 1) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (z1 + 1) * dx +hol_form (z1 + 1) * dx +(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx +hol_form (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx +(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (z0) * dx +hol_form (z0) * dx +(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0*z1 + z0) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (z0*z1 + z0) * dx +hol_form (z0*z1 + z0) * dx +(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (z0^2) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (z0^2) * dx +hol_form (z0^2) * dx +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (x) * dx +hol_form (x) * dx +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x*z0^2 + x*z1 + x) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (-x*z0^2 + x*z1 + x) * dx +hol_form (-x*z0^2 + x*z1 + x) * dx +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x*z0) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (x*z0) * dx +hol_form (x*z0) * dx +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2) * dx, 0 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 0 +0 q r: 0 0 +if 0 True +omega - df (x^2) * dx +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (0) * dx, (z1 + 1)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 1/x +1/x q r: 0 1 +if 1/x True +omega - df (1/x^2) * dx +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x^2*z1 - x^2) * dx, (z1^2 - z1 + 1)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? 1/x +1/x q r: 0 1 +if 1/x True +omega - df ((-x^4 + 1)/x^2) * dx +hol_form (-x^2) * dx +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2*z0) * dx, (z0*z1 + z0)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? z0/x +z0/x q r: 0 z0 +if z0/x True +omega - df ((-x^2 + z0)/x^2) * dx +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x^2*z0*z1 + z0^2*z1 + z0^2) * dx, (z0*z1^2 - z0*z1 + z0)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? z0/x +z0/x q r: 0 z0 +if z0/x True +omega - df ((x^2*z0^2 - x^2 + z0)/x^2) * dx +hol_form (z0^2) * dx +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (x^2*z0^2) * dx, (z0^2*z1 + z0^2)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? (z0^2 - z1)/x +(z0^2 - z1)/x q r: 0 z0^2 - z1 +if (z0^2 - z1)/x True +omega - df ((-x^4 + x^2*z0 + z0^2 - z1)/x^2) * dx +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x^2*z0^2*z1 - x^2*z0^2 + z0*z1^2 - z0*z1 + z0) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? (z0^2 - z1)/x +(z0^2 - z1)/x q r: 0 z0^2 - z1 +if (z0^2 - z1)/x True +omega - df ((-x^4 - x^2*z0*z1 - x^2*z0 + z0^2 - z1)/x^2) * dx +hol_form (-z0*z1 + z0) * dx +(-z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x*z0^2) * dx, (z1^2 - z1 + 1)/x^2 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? (-z1 + 1)/x^2 +(-z1 + 1)/x^2 q r: 0 -z1 + 1 +if (-z1 + 1)/x^2 True +omega - df ((-x^4 + z1 - 1)/x^3) * dx +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x*z0*z1 - x*z0) * dx, (z0*z1^2 - z0*z1 + z0)/x^2 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? (-z0*z1 + z0)/x^2 +(-z0*z1 + z0)/x^2 q r: 0 -z0*z1 + z0 +if (-z0*z1 + z0)/x^2 True +omega - df ((x^4*z0 + x^2*z1 - x^2 + z0*z1 - z0)/x^3) * dx +hol_form (-x*z0) * dx +(-x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +nowe!!!! ( (-x*z0^2*z1) * dx, (z0^2*z1^2 - z0^2*z1 + z0^2)/x^2 ) +products: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +? (-z0^2*z1 + z0^2 - z1^2)/x^2 +(-z0^2*z1 + z0^2 - z1^2)/x^2 q r: 0 -z0^2*z1 + z0^2 - z1^2 +if (-z0^2*z1 + z0^2 - z1^2)/x^2 False +omega - df ((-x^4*z0^2 + x^4*z1 - x^2*z0*z1 + x^2*z0 + z0^2*z1 - z0^2 + z1^2)/x^3) * dx +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Input In [48], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :84, in coordinates(self, threshold, basis) + +ValueError: I arrived at a form (omega, 0), in which omega is not regular on U0. I hoped this wouldn t happen. +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +omega val 0 +z1^2/x +omega val 12 +z0*z1/x +omega val 6 +z0*z1^2/x +omega val 2 +z0^2*z1/x +omega val 0 +z0^2*z1^2/x +omega val 0 +z1^2/x^2 +omega val 1 +z0*z1^2/x^2 +omega val 3 +z0^2*z1^2/x^2 +omega val 1 +z0^2*z1^2/x^3 +omega val 6 +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 - z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Input In [49], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :77, in coordinates(self, threshold, basis) + +ValueError: I arrived at a form (omega, 0), in which omega is not regular on U0. I hoped this wouldn t happen. +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lhomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7lsage: AS.cohomology_of_structure_sheaf_basis()[1] +[?7h[?12l[?25h[?2004l[?7hz1^2/x +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor i, f in enumerate(AS.cohomology_of_structure_sheaf_basis()):[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ln[?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[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?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[?7lsage: for eta in AS.de_rham_basis(): +....: [?7h[?12l[?25h[?25l[?7lprint(om.serre_duality_pairing(f))[?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[?7le[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?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[?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....:  print(eta.omega0, eta.omega8.valuation()) +....: [?7h[?12l[?25h[?25l[?7lsage: for eta in AS.de_rham_basis(): +....:  print(eta.omega0, eta.omega8.valuation()) +....:  +[?7h[?12l[?25h[?2004lz1/x +omega val 0 +z1^2/x +omega val 12 +z0*z1/x +omega val 6 +z0*z1^2/x +omega val 2 +z0^2*z1/x +omega val 0 +z0^2*z1^2/x +omega val 0 +z1^2/x^2 +omega val 1 +z0*z1^2/x^2 +omega val 3 +z0^2*z1^2/x^2 +omega val 1 +z0^2*z1^2/x^3 +omega val 6 +(1) * dx 18 +(z1) * dx 6 +(x^2*z0 + z0^2*z1 + z1^2) * dx 2 +(z0) * dx 12 +(z0*z1) * dx 0 +(z0^2) * dx 6 +(x) * dx 9 +(-x*z0^2 + x*z1) * dx 1 +(x*z0) * dx 3 +(x^2) * dx 0 +(0) * dx 0 +(x^2*z1) * dx 12 +(-x^2*z0) * dx 6 +(x^2*z0*z1 - x^2*z0 - z0^2*z1) * dx 2 +(-x^2*z0^2) * dx 0 +(x^2*z0^2*z1 - z0*z1^2) * dx 0 +(x*z0^2) * dx 1 +(x*z0*z1) * dx 3 +(x*z0^2*z1 - x*z0^2) * dx 1 +(z0^2*z1) * dx 6 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for eta in AS.de_rham_basis(): +....:  print(eta.omega0, eta.omega8.valuation())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lAS.cohomology_ofstructure_sheaf_basis()[1] + [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +hol_form (1) * dx +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +hol_form (z1) * dx +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +hol_form (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +hol_form (z0 + 1) * dx +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +hol_form (z0*z1 + z1) * dx +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +hol_form (z0^2 - z0 + 1) * dx +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +hol_form (x) * dx +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +hol_form (x*z0 + x) * dx +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +hol_form (-x^2) * dx +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +hol_form (-x^2 + z0*z1 - z1) * dx +(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +hol_form (-x^2) * dx +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +hol_form (-x^2*z0 - z0^2*z1 - z1^2) * dx +(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +hol_form (-x*z0 + x) * dx +(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +hol_form (-x*z0^2 + x*z1) * dx +(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +hol_form (-z0*z1 + z1) * dx +(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +hol_form (1) * dx +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +hol_form (z1 + 1) * dx +(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +hol_form (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx +(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +hol_form (z0) * dx +(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +hol_form (z0*z1 + z0) * dx +(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +hol_form (z0^2) * dx +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +hol_form (x) * dx +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +hol_form (-x*z0^2 + x*z1 + x) * dx +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +hol_form (x*z0) * dx +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +hol_form (-z0^2) * dx +(-z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +hol_form (z0*z1 - z0) * dx +(z0*z1 - z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +hol_form (x*z0) * dx +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Input In [52], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :78, in coordinates(self, threshold, basis) + +ValueError: I arrived at a form (omega, 0), in which omega is not regular on U0. I hoped this wouldn t happen. +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lhlrphic_differential_bsis()[1].group_action([0, 1])[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lomorphic_differentials_basis()[1].group_action([0, 1])[?7h[?12l[?25h[?25l[?7l([][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls()[1].group_action([0, 1])[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis() +[?7h[?12l[?25h[?2004l[?7h[(1) * dx, + (z1) * dx, + (x^2*z0 + z0^2*z1 + z1^2) * dx, + (z0) * dx, + (z0*z1) * dx, + (z0^2) * dx, + (x) * dx, + (-x*z0^2 + x*z1) * dx, + (x*z0) * dx, + (x^2) * dx] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] + +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +( (1) * dx, 0 ) +hol_form (1) * dx +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +( (z1) * dx, 0 ) +hol_form (z1) * dx +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) +hol_form (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +( (z0 + 1) * dx, 0 ) +hol_form (z0 + 1) * dx +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +( (z0*z1 + z1) * dx, 0 ) +hol_form (z0*z1 + z1) * dx +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +( (z0^2 - z0 + 1) * dx, 0 ) +hol_form (z0^2 - z0 + 1) * dx +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +( (x) * dx, 0 ) +hol_form (x) * dx +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) +hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +( (x*z0 + x) * dx, 0 ) +hol_form (x*z0 + x) * dx +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +( (x^2) * dx, 0 ) +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +( (0) * dx, 0 ) +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +( (0) * dx, 0 ) +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +( (-x^2) * dx, 0 ) +hol_form (-x^2) * dx +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +( (-x^2 + z0*z1 - z1) * dx, 0 ) +hol_form (-x^2 + z0*z1 - z1) * dx +(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +( (-x^2) * dx, 0 ) +hol_form (-x^2) * dx +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +( (-x^2*z0 - z0^2*z1 - z1^2) * dx, 0 ) +hol_form (-x^2*z0 - z0^2*z1 - z1^2) * dx +(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +( (-x*z0 + x) * dx, 0 ) +hol_form (-x*z0 + x) * dx +(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +( (-x*z0^2 + x*z1) * dx, 0 ) +hol_form (-x*z0^2 + x*z1) * dx +(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) +hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +( (-z0*z1 + z1) * dx, (x^2*z1 - z0*z1^2 + z1^2)/x^3 ) +hol_form (-z0*z1 + z1) * dx +(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +( (1) * dx, 0 ) +hol_form (1) * dx +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +( (z1 + 1) * dx, 0 ) +hol_form (z1 + 1) * dx +(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +( (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx, 0 ) +hol_form (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx +(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +( (z0) * dx, 0 ) +hol_form (z0) * dx +(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +( (z0*z1 + z0) * dx, 0 ) +hol_form (z0*z1 + z0) * dx +(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +( (z0^2) * dx, 0 ) +hol_form (z0^2) * dx +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +( (x) * dx, 0 ) +hol_form (x) * dx +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +( (-x*z0^2 + x*z1 + x) * dx, 0 ) +hol_form (-x*z0^2 + x*z1 + x) * dx +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +( (x*z0) * dx, 0 ) +hol_form (x*z0) * dx +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +( (x^2) * dx, 0 ) +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +( (0) * dx, 1/x ) +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +( (x^2) * dx, 1/x ) +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +( (0) * dx, z0/x ) +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +( (-z0^2) * dx, z0/x ) +hol_form (-z0^2) * dx +(-z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +( (0) * dx, (z0^2 - z1)/x ) +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +( (z0*z1 - z0) * dx, (z0^2 - z1)/x ) +hol_form (z0*z1 - z0) * dx +(z0*z1 - z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +( (0) * dx, (-z1 + 1)/x^2 ) +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +( (x*z0) * dx, (-z0*z1 + z0)/x^2 ) +hol_form (x*z0) * dx +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +( (0) * dx, (-z0^2*z1 + z0^2 - z1^2)/x^2 ) +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Input In [54], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :79, in coordinates(self, threshold, basis) + +ValueError: I arrived at a form (omega, 0), in which omega is not regular on U0. I hoped this wouldn t happen. +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-z0^2*z1 + z0^2 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAx^2[?7h[?12l[?25h[?25l[?7lSx^2[?7h[?12l[?25h[?25l[?7l.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAz1^2)/AS.x^2[?7h[?12l[?25h[?25l[?7lSz1^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l.z1^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAz0^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7lSz0^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l.z0^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[0^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAz0^2*z1 + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7lSz0^2*z1 + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l.z0^2*z1 + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[0^2*z1 + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]^2*z1 + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAz1 + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7lSz1 + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l.z1 + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1 + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[] + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (-AS.z[0]^2*AS.z[1] + AS.z[0]^2 - AS.z[1]^2)/AS.x^2 +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [55], in () +----> 1 (-AS.z[Integer(0)]**Integer(2)*AS.z[Integer(1)] + AS.z[Integer(0)]**Integer(2) - AS.z[Integer(1)]**Integer(2))/AS.x**Integer(2) + +TypeError: bad operand type for unary -: 'as_function' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-AS.z[0]^2*AS.z[1] + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1AS.z[0]^2*AS.z[1] + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-1AS.z[0]^2*AS.z[1] + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()AS.z[0]^2*AS.z[1] + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l()*AS.z[0]^2*AS.z[1] + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((-1)*AS.z[0]^2*AS.z[1] + AS.z[0]^2 - AS.z[1]^2)/AS.x^2 +[?7h[?12l[?25h[?2004l[?7h(-z0^2*z1 + z0^2 - z1^2)/x^2 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((-1)*AS.z[0]^2*AS.z[1] + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?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)*AS.z[0]^2*AS.z[1] + AS.z[0]^2 - AS.z[1]^2)/AS.x^2)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?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[?7lsage: (((-1)*AS.z[0]^2*AS.z[1] + AS.z[0]^2 - AS.z[1]^2)/AS.x^2).expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7ht^-6 + 2*t^2 + 2*t^10 + 2*t^14 + 2*t^18 + t^26 + 2*t^30 + 2*t^38 + 2*t^46 + 2*t^54 + t^58 + t^62 + t^66 + 2*t^78 + 2*t^90 + 2*t^94 + t^98 + 2*t^102 + t^118 + t^122 + 2*t^134 + 2*t^138 + 2*t^142 + 2*t^146 + 2*t^154 + t^158 + 2*t^162 + 2*t^166 + t^170 + 2*t^182 + 2*t^186 + t^190 + 2*t^202 + 2*t^206 + 2*t^218 + t^222 + t^230 + 2*t^234 + t^238 + t^246 + 2*t^250 + 2*t^262 + 2*t^266 + t^278 + 2*t^282 + t^286 + 2*t^298 + t^310 + 2*t^314 + 2*t^318 + t^326 + 2*t^330 + 2*t^334 + t^338 + 2*t^346 + t^350 + t^354 + t^370 + 2*t^374 + t^382 + 2*t^386 + t^390 + 2*t^394 + t^402 + 2*t^410 + 2*t^414 + t^418 + t^422 + t^426 + 2*t^434 + t^446 + 2*t^450 + t^458 + 2*t^462 + t^466 + 2*t^470 + 2*t^474 + 2*t^478 + 2*t^482 + 2*t^486 + t^490 + t^494 + t^498 + 2*t^510 + 2*t^514 + t^522 + 2*t^526 + 2*t^530 + 2*t^538 + 2*t^542 + 2*t^546 + 2*t^554 + 2*t^558 + 2*t^562 + 2*t^574 + 2*t^578 + 2*t^586 + 2*t^590 + 2*t^594 + 2*t^602 + 2*t^606 + 2*t^610 + t^618 + 2*t^622 + 2*t^638 + 2*t^642 + 2*t^650 + 2*t^654 + 2*t^670 + t^682 + 2*t^686 + 2*t^698 + 2*t^702 + t^714 + 2*t^718 + t^730 + 2*t^734 + t^746 + 2*t^750 + t^762 + 2*t^766 + 2*t^770 + t^778 + 2*t^782 + 2*t^786 + 2*t^798 + 2*t^802 + 2*t^814 + t^818 + t^826 + 2*t^830 + 2*t^834 + t^842 + 2*t^846 + 2*t^850 + t^858 + 2*t^862 + 2*t^866 + t^874 + 2*t^878 + 2*t^882 + t^890 + 2*t^894 + 2*t^898 + t^906 + 2*t^910 + t^914 + t^922 + 2*t^926 + t^930 + 2*t^942 + t^946 + 2*t^958 + 2*t^966 + t^970 + t^978 + t^982 + 2*t^986 + O(t^994) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1] + AS.z[0]^2 - AS.z[1]^2)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: (((-1)*AS.z[0]^2*AS.z[1] + AS.z[0]^2)/AS.x^2).expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7h2*t^-6 + 2*t^-2 + 2*t^6 + t^10 + 2*t^14 + t^18 + 2*t^22 + t^30 + 2*t^34 + 2*t^38 + t^46 + 2*t^50 + t^54 + 2*t^58 + t^70 + t^74 + t^82 + t^86 + t^90 + t^98 + 2*t^102 + 2*t^106 + t^114 + t^122 + 2*t^126 + 2*t^130 + t^134 + t^138 + 2*t^146 + t^154 + t^162 + t^166 + t^174 + t^178 + 2*t^182 + t^194 + t^198 + 2*t^206 + t^210 + 2*t^214 + t^222 + t^226 + t^242 + t^246 + t^258 + t^270 + t^274 + 2*t^278 + t^286 + t^290 + t^294 + t^302 + t^306 + 2*t^322 + 2*t^326 + t^330 + 2*t^338 + 2*t^342 + t^346 + t^350 + 2*t^358 + t^362 + 2*t^366 + t^374 + 2*t^378 + 2*t^382 + t^386 + 2*t^394 + t^398 + t^402 + t^406 + 2*t^410 + t^414 + t^418 + t^422 + 2*t^430 + t^434 + t^438 + t^442 + t^446 + 2*t^454 + 2*t^458 + t^462 + 2*t^470 + t^478 + t^486 + t^490 + t^502 + 2*t^506 + 2*t^514 + t^518 + t^534 + t^546 + t^550 + t^554 + t^566 + t^582 + t^586 + t^594 + t^598 + t^602 + t^610 + t^614 + 2*t^618 + t^626 + t^630 + t^642 + t^646 + t^650 + t^662 + 2*t^666 + t^674 + t^678 + t^694 + t^698 + 2*t^706 + t^710 + 2*t^722 + t^726 + 2*t^738 + t^742 + t^754 + t^758 + 2*t^762 + t^770 + t^774 + 2*t^778 + t^790 + 2*t^794 + t^806 + t^810 + 2*t^818 + t^822 + t^826 + 2*t^834 + t^838 + t^842 + 2*t^850 + t^854 + t^858 + 2*t^866 + t^870 + t^874 + 2*t^882 + t^886 + t^890 + t^898 + t^902 + t^914 + t^918 + t^934 + t^950 + 2*t^954 + 2*t^962 + 2*t^966 + 2*t^990 + O(t^994) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1] + AS.z[0]^2)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?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)*AS.z[0]^2*AS.z[1] + AS.z[0]^2 - AS.z[1]^2)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l-1)*AS.z[0]^2*AS.z[1] + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l-AS.z[0]^2*AS.z[1] + AS.z[0]^2 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +--------------------------------------------------------------------------- +IndexError Traceback (most recent call last) +Input In [59], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :55, in coordinates(self, threshold, basis) + +IndexError: list assignment index out of range +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [60], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :61, in coordinates(self, threshold, basis) + +File :61, in (.0) + +File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:493, in sage.modules.free_module_element.vector() + 491 pass + 492 else: +--> 493 v = arg0_vector_(arg1) + 494 if immutable: + 495 v.set_immutable() + +TypeError: IntegerMod_int._vector_() takes no arguments (1 given) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +[0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2] +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [61], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :61, in coordinates(self, threshold, basis) + +File :61, in (.0) + +File /ext/sage/9.7/src/sage/modules/free_module_element.pyx:493, in sage.modules.free_module_element.vector() + 491 pass + 492 else: +--> 493 v = arg0_vector_(arg1) + 494 if immutable: + 495 v.set_immutable() + +TypeError: IntegerMod_int._vector_() takes no arguments (1 given) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (1) * dx, 0 ) [] +hol_form (1) * dx +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (z1) * dx, 0 ) [] +hol_form (z1) * dx +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) [] +hol_form (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (z0 + 1) * dx, 0 ) [] +hol_form (z0 + 1) * dx +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (z0*z1 + z1) * dx, 0 ) [] +hol_form (z0*z1 + z1) * dx +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (z0^2 - z0 + 1) * dx, 0 ) [] +hol_form (z0^2 - z0 + 1) * dx +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (x) * dx, 0 ) [] +hol_form (x) * dx +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) [] +hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (x*z0 + x) * dx, 0 ) [] +hol_form (x*z0 + x) * dx +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (x^2) * dx, 0 ) [] +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (0) * dx, 0 ) [] +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (0) * dx, 0 ) [] +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-x^2) * dx, 0 ) [] +hol_form (-x^2) * dx +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-x^2 + z0*z1 - z1) * dx, 0 ) [] +hol_form (-x^2 + z0*z1 - z1) * dx +(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-x^2) * dx, 0 ) [] +hol_form (-x^2) * dx +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-x^2*z0 - z0^2*z1 - z1^2) * dx, 0 ) [] +hol_form (-x^2*z0 - z0^2*z1 - z1^2) * dx +(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-x*z0 + x) * dx, 0 ) [] +hol_form (-x*z0 + x) * dx +(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-x*z0^2 + x*z1) * dx, 0 ) [] +hol_form (-x*z0^2 + x*z1) * dx +(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) [] +hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-z0*z1 + z1) * dx, (x^2*z1 - z0*z1^2 + z1^2)/x^3 ) [] +--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Input In [62], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :70, in coordinates(self, threshold, basis) + +NameError: name 'v_f_den' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (1) * dx, 0 ) [] +--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +File /ext/sage/9.7/src/sage/rings/fraction_field.py:706, in FractionField_generic._element_constructor_(self, x, y, coerce) + 705 try: +--> 706 x, y = resolve_fractions(x0, y0) + 707 except (AttributeError, TypeError): + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:683, in FractionField_generic._element_constructor_..resolve_fractions(x, y) + 682 def resolve_fractions(x, y): +--> 683 xn = x.numerator() + 684 xd = x.denominator() + +AttributeError: 'function' object has no attribute 'numerator' + +During handling of the above exception, another exception occurred: + +TypeError Traceback (most recent call last) +Input In [63], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :69, in coordinates(self, threshold, basis) + +File :14, in __init__(self, C, g) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 159 print(type(C), C) + 160 print(type(C._element_constructor), C._element_constructor) +--> 161 raise + 162 + 163 cpdef Element _call_with_args(self, x, args=(), kwds={}): + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 154 cdef Parent C = self._codomain + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + 158 if print_warnings: + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:708, in FractionField_generic._element_constructor_(self, x, y, coerce) + 706 x, y = resolve_fractions(x0, y0) + 707 except (AttributeError, TypeError): +--> 708 raise TypeError("cannot convert {!r}/{!r} to an element of {}".format( + 709 x0, y0, self)) + 710 try: + 711 return self._element_class(self, x, y, coerce=coerce) + +TypeError: cannot convert /1 to an element of Fraction Field of Multivariate Polynomial Ring in x, y, z0, z1 over Finite Field of size 3 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (1) * dx, 0 ) [] +hol_form (1) * dx +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (z1) * dx, 0 ) [] +hol_form (z1) * dx +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) [] +hol_form (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (z0 + 1) * dx, 0 ) [] +hol_form (z0 + 1) * dx +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (z0*z1 + z1) * dx, 0 ) [] +hol_form (z0*z1 + z1) * dx +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (z0^2 - z0 + 1) * dx, 0 ) [] +hol_form (z0^2 - z0 + 1) * dx +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (x) * dx, 0 ) [] +hol_form (x) * dx +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) [] +hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (x*z0 + x) * dx, 0 ) [] +hol_form (x*z0 + x) * dx +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (x^2) * dx, 0 ) [] +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (0) * dx, 0 ) [] +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (0) * dx, 0 ) [] +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-x^2) * dx, 0 ) [] +hol_form (-x^2) * dx +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-x^2 + z0*z1 - z1) * dx, 0 ) [] +hol_form (-x^2 + z0*z1 - z1) * dx +(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-x^2) * dx, 0 ) [] +hol_form (-x^2) * dx +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-x^2*z0 - z0^2*z1 - z1^2) * dx, 0 ) [] +hol_form (-x^2*z0 - z0^2*z1 - z1^2) * dx +(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-x*z0 + x) * dx, 0 ) [] +hol_form (-x*z0 + x) * dx +(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-x*z0^2 + x*z1) * dx, 0 ) [] +hol_form (-x*z0^2 + x*z1) * dx +(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) [] +hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-z0*z1 + z1) * dx, (x^2*z1 - z0*z1^2 + z1^2)/x^3 ) [] +hol_form (-z0*z1 + z1) * dx +(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (1) * dx, 0 ) [] +hol_form (1) * dx +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (z1 + 1) * dx, 0 ) [] +hol_form (z1 + 1) * dx +(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx, 0 ) [] +hol_form (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx +(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (z0) * dx, 0 ) [] +hol_form (z0) * dx +(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (z0*z1 + z0) * dx, 0 ) [] +hol_form (z0*z1 + z0) * dx +(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (z0^2) * dx, 0 ) [] +hol_form (z0^2) * dx +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (x) * dx, 0 ) [] +hol_form (x) * dx +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-x*z0^2 + x*z1 + x) * dx, 0 ) [] +hol_form (-x*z0^2 + x*z1 + x) * dx +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (x*z0) * dx, 0 ) [] +hol_form (x*z0) * dx +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (x^2) * dx, 0 ) [] +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (0) * dx, 1/x ) [] +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (x^2) * dx, 1/x ) [] +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (0) * dx, z0/x ) [] +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-z0^2) * dx, z0/x ) [] +hol_form (-z0^2) * dx +(-z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (0) * dx, (z0^2 - z1)/x ) [] +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (z0*z1 - z0) * dx, (z0^2 - z1)/x ) [] +hol_form (z0*z1 - z0) * dx +(z0*z1 - z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (0) * dx, (-z1 + 1)/x^2 ) [] +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (x*z0) * dx, (-z0*z1 + z0)/x^2 ) [] +hol_form (x*z0) * dx +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (0) * dx, (-z0^2*z1 + z0^2 - z1^2)/x^2 ) [] +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Input In [64], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :82, in coordinates(self, threshold, basis) + +ValueError: I arrived at a form (omega, 0), in which omega is not regular on U0. I hoped this wouldn t happen. +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1] + AS.z[0]^2)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l - AS.z[1]^2)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1] + AS.z[0]^2)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (1) * dx, 0 ) [] +hol_form (1) * dx +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (z1) * dx, 0 ) [] +hol_form (z1) * dx +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) [] +hol_form (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (z0 + 1) * dx, 0 ) [] +hol_form (z0 + 1) * dx +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (z0*z1 + z1) * dx, 0 ) [] +hol_form (z0*z1 + z1) * dx +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (z0^2 - z0 + 1) * dx, 0 ) [] +hol_form (z0^2 - z0 + 1) * dx +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (x) * dx, 0 ) [] +hol_form (x) * dx +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) [] +hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (x*z0 + x) * dx, 0 ) [] +hol_form (x*z0 + x) * dx +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (x^2) * dx, 0 ) [] +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (0) * dx, 0 ) [] +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (0) * dx, 0 ) [] +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-x^2) * dx, 0 ) [] +hol_form (-x^2) * dx +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-x^2 + z0*z1 - z1) * dx, 0 ) [] +hol_form (-x^2 + z0*z1 - z1) * dx +(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-x^2) * dx, 0 ) [] +hol_form (-x^2) * dx +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-x^2*z0 - z0^2*z1 - z1^2) * dx, 0 ) [] +hol_form (-x^2*z0 - z0^2*z1 - z1^2) * dx +(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-x*z0 + x) * dx, 0 ) [] +hol_form (-x*z0 + x) * dx +(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-x*z0^2 + x*z1) * dx, 0 ) [] +hol_form (-x*z0^2 + x*z1) * dx +(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) [] +hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-z0*z1 + z1) * dx, (x^2*z1 - z0*z1^2 + z1^2)/x^3 ) [] +hol_form (-z0*z1 + z1) * dx +(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (1) * dx, 0 ) [] +hol_form (1) * dx +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (z1 + 1) * dx, 0 ) [] +hol_form (z1 + 1) * dx +(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx, 0 ) [] +hol_form (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx +(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (z0) * dx, 0 ) [] +hol_form (z0) * dx +(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (z0*z1 + z0) * dx, 0 ) [] +hol_form (z0*z1 + z0) * dx +(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (z0^2) * dx, 0 ) [] +hol_form (z0^2) * dx +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (x) * dx, 0 ) [] +hol_form (x) * dx +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-x*z0^2 + x*z1 + x) * dx, 0 ) [] +hol_form (-x*z0^2 + x*z1 + x) * dx +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (x*z0) * dx, 0 ) [] +hol_form (x*z0) * dx +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (x^2) * dx, 0 ) [] +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (0) * dx, 1/x ) [] +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (x^2) * dx, 1/x ) [] +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (0) * dx, z0/x ) [] +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-z0^2) * dx, z0/x ) [] +hol_form (-z0^2) * dx +(-z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (0) * dx, (z0^2 - z1)/x ) [] +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (z0*z1 - z0) * dx, (z0^2 - z1)/x ) [] +hol_form (z0*z1 - z0) * dx +(z0*z1 - z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (0) * dx, (-z1 + 1)/x^2 ) [] +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (x*z0) * dx, (-z0*z1 + z0)/x^2 ) [] +hol_form (x*z0) * dx +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (0) * dx, (-z0^2*z1 + z0^2 - z1^2)/x^2 ) [] +( (0) * dx, (-z0^2*z1 - z1^2)/x^2 ) +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Input In [65], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :83, in coordinates(self, threshold, basis) + +ValueError: I arrived at a form (omega, 0), in which omega is not regular on U0. I hoped this wouldn t happen. +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.quo_rem(f)[?7h[?12l[?25h[?25l[?7lg =[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAx^2[?7h[?12l[?25h[?25l[?7lSx^2[?7h[?12l[?25h[?25l[?7l.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAz1^2)/AS.x^2[?7h[?12l[?25h[?25l[?7lSz1^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l.z1^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lAz0^2*z1 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7lSz0^2*z1 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l.z0^2*z1 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[0^2*z1 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]^2*z1 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAz1 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7lSz1 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l/z1 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz1 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l.z1 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1 - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[] - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (-AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2 +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [66], in () +----> 1 (-AS.z[Integer(0)]**Integer(2)*AS.z[Integer(1)] - AS.z[Integer(1)]**Integer(2))/AS.x**Integer(2) + +TypeError: bad operand type for unary -: 'as_function' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l()AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-1)AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((-1)AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2 +[?7h[?12l[?25h[?2004l Input In [67] + ((-Integer(1))AS.z[Integer(0)]**Integer(2)*AS.z[Integer(1)] - AS.z[Integer(1)]**Integer(2))/AS.x**Integer(2) + ^ +SyntaxError: invalid syntax. Perhaps you forgot a comma? + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((-1)AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7lsage: ((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2 +[?7h[?12l[?25h[?2004l[?7h(-z0^2*z1 - z1^2)/x^2 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l2.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lnsion[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2.expansion_at_infty() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Input In [69], in () +----> 1 ((-Integer(1))*AS.z[Integer(0)]**Integer(2)*AS.z[Integer(1)] - AS.z[Integer(1)]**Integer(2))/AS.x**Integer(2).expansion_at_infty() + +File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() + 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' + 493 """ +--> 494 return self.getattr_from_category(name) + 495 + 496 cdef getattr_from_category(self, name): + +File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() + 505 else: + 506 cls = P._abstract_element_class +--> 507 return getattr_from_other_class(self, cls, name) + 508 + 509 def __dir__(self): + +File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() + 359 dummy_error_message.cls = type(self) + 360 dummy_error_message.name = name +--> 361 raise AttributeError(dummy_error_message) + 362 attribute = attr + 363 # Check for a descriptor (__get__ in Python) + +AttributeError: 'sage.rings.integer.Integer' object has no attribute 'expansion_at_infty' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?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)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: (((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2).expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7ht^-6 + 2*t^2 + 2*t^6 + 2*t^10 + 2*t^14 + 2*t^18 + 2*t^22 + t^26 + 2*t^30 + t^38 + 2*t^42 + 2*t^46 + 2*t^54 + t^62 + t^66 + 2*t^74 + t^98 + 2*t^102 + t^106 + t^110 + 2*t^114 + t^118 + 2*t^122 + t^126 + 2*t^130 + 2*t^134 + 2*t^138 + t^146 + 2*t^154 + 2*t^158 + 2*t^162 + 2*t^166 + t^170 + t^174 + 2*t^182 + 2*t^190 + 2*t^198 + 2*t^214 + t^246 + 2*t^254 + 2*t^262 + 2*t^270 + t^278 + t^294 + 2*t^302 + 2*t^310 + t^318 + 2*t^326 + t^330 + t^334 + t^338 + t^342 + t^346 + t^354 + t^358 + 2*t^362 + 2*t^366 + t^370 + t^378 + 2*t^386 + t^390 + 2*t^398 + t^422 + 2*t^426 + t^430 + t^434 + 2*t^438 + t^442 + 2*t^446 + t^450 + 2*t^454 + 2*t^458 + 2*t^462 + t^470 + 2*t^474 + 2*t^478 + t^482 + 2*t^486 + t^490 + t^494 + t^514 + t^522 + t^530 + 2*t^538 + 2*t^546 + 2*t^554 + 2*t^562 + t^570 + 2*t^578 + 2*t^618 + t^626 + t^634 + t^658 + t^666 + t^674 + 2*t^682 + 2*t^762 + 2*t^770 + 2*t^778 + 2*t^786 + t^794 + 2*t^802 + 2*t^810 + t^818 + 2*t^906 + 2*t^914 + 2*t^922 + 2*t^930 + t^938 + 2*t^946 + 2*t^954 + t^962 + 2*t^966 + t^974 + t^978 + t^982 + t^986 + t^990 + O(t^994) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_atinfty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: (((-1)*AS.z[0]^2*AS.z[1])/AS.x^2).expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7h2*t^-6 + 2*t^-2 + t^6 + t^10 + 2*t^14 + t^18 + t^22 + t^30 + 2*t^34 + t^38 + 2*t^42 + t^46 + 2*t^50 + t^54 + t^58 + t^70 + t^78 + t^82 + t^86 + 2*t^90 + t^94 + t^98 + 2*t^102 + t^110 + 2*t^122 + t^130 + t^134 + t^138 + t^142 + t^146 + t^154 + t^158 + t^162 + t^166 + 2*t^174 + t^178 + 2*t^182 + t^186 + t^190 + t^194 + t^202 + t^210 + t^214 + t^218 + t^226 + 2*t^230 + t^234 + 2*t^238 + t^242 + t^246 + t^250 + 2*t^254 + t^258 + t^266 + t^274 + 2*t^278 + t^282 + t^290 + 2*t^294 + t^298 + t^306 + t^310 + t^314 + 2*t^318 + 2*t^322 + 2*t^334 + 2*t^338 + t^366 + 2*t^374 + t^382 + t^386 + t^406 + 2*t^414 + t^422 + t^426 + 2*t^442 + 2*t^446 + 2*t^450 + t^454 + t^462 + 2*t^466 + t^470 + t^478 + 2*t^482 + t^486 + t^490 + 2*t^498 + t^502 + 2*t^506 + t^510 + t^514 + t^518 + t^526 + 2*t^530 + t^534 + t^542 + t^546 + t^550 + t^554 + t^558 + t^566 + t^570 + t^574 + t^582 + 2*t^586 + t^590 + 2*t^594 + t^598 + 2*t^602 + t^606 + 2*t^610 + t^614 + t^622 + 2*t^626 + t^630 + t^634 + t^638 + 2*t^642 + t^646 + 2*t^650 + t^654 + t^658 + t^662 + t^670 + 2*t^674 + t^678 + t^682 + t^686 + t^694 + 2*t^698 + t^702 + 2*t^706 + t^710 + 2*t^714 + t^718 + 2*t^722 + t^726 + 2*t^730 + t^734 + 2*t^738 + t^742 + 2*t^746 + t^750 + t^754 + t^758 + t^766 + t^770 + t^774 + t^782 + t^790 + t^798 + t^806 + t^814 + 2*t^818 + t^822 + t^830 + t^838 + t^846 + t^854 + t^862 + t^870 + t^878 + t^886 + t^894 + 2*t^898 + t^902 + t^906 + t^910 + 2*t^914 + t^918 + t^922 + t^926 + t^930 + t^934 + t^938 + t^942 + t^946 + t^950 + t^954 + t^958 + 2*t^966 + 2*t^970 + t^974 + 2*t^986 + O(t^994) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1])/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l - AS.z[1]^2)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().expansion_at_infty()[?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: (((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2).diffn() +[?7h[?12l[?25h[?2004l[?7h((x^4*z0^2 - x^4*z1 + x^2*z0*z1 - z0^2*z1 - z1^2)/x^3) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2).diffn()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_nty()[?7h[?12l[?25h[?25l[?7l - AS.z[1]^2)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lAS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l-AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1] + AS.z[0]^2)/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (1) * dx, 0 ) [] +hol_form (1) * dx +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (z1) * dx, 0 ) [] +hol_form (z1) * dx +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) [] +hol_form (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (z0 + 1) * dx, 0 ) [] +hol_form (z0 + 1) * dx +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (z0*z1 + z1) * dx, 0 ) [] +hol_form (z0*z1 + z1) * dx +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (z0^2 - z0 + 1) * dx, 0 ) [] +hol_form (z0^2 - z0 + 1) * dx +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (x) * dx, 0 ) [] +hol_form (x) * dx +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) [] +hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (x*z0 + x) * dx, 0 ) [] +hol_form (x*z0 + x) * dx +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (x^2) * dx, 0 ) [] +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (0) * dx, 0 ) [] +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (0) * dx, 0 ) [] +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-x^2) * dx, 0 ) [] +hol_form (-x^2) * dx +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-x^2 + z0*z1 - z1) * dx, 0 ) [] +hol_form (-x^2 + z0*z1 - z1) * dx +(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-x^2) * dx, 0 ) [] +hol_form (-x^2) * dx +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-x^2*z0 - z0^2*z1 - z1^2) * dx, 0 ) [] +hol_form (-x^2*z0 - z0^2*z1 - z1^2) * dx +(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-x*z0 + x) * dx, 0 ) [] +hol_form (-x*z0 + x) * dx +(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-x*z0^2 + x*z1) * dx, 0 ) [] +hol_form (-x*z0^2 + x*z1) * dx +(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) [] +hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-z0*z1 + z1) * dx, (x^2*z1 - z0*z1^2 + z1^2)/x^3 ) [] +hol_form (-z0*z1 + z1) * dx +(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (1) * dx, 0 ) [] +hol_form (1) * dx +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (z1 + 1) * dx, 0 ) [] +hol_form (z1 + 1) * dx +(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx, 0 ) [] +hol_form (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx +(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (z0) * dx, 0 ) [] +hol_form (z0) * dx +(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (z0*z1 + z0) * dx, 0 ) [] +hol_form (z0*z1 + z0) * dx +(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (z0^2) * dx, 0 ) [] +hol_form (z0^2) * dx +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (x) * dx, 0 ) [] +hol_form (x) * dx +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-x*z0^2 + x*z1 + x) * dx, 0 ) [] +hol_form (-x*z0^2 + x*z1 + x) * dx +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (x*z0) * dx, 0 ) [] +hol_form (x*z0) * dx +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (x^2) * dx, 0 ) [] +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (0) * dx, 1/x ) [] +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (x^2) * dx, 1/x ) [] +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (0) * dx, z0/x ) [] +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-z0^2) * dx, z0/x ) [] +hol_form (-z0^2) * dx +(-z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (0) * dx, (z0^2 - z1)/x ) [] +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (z0*z1 - z0) * dx, (z0^2 - z1)/x ) [] +hol_form (z0*z1 - z0) * dx +(z0*z1 - z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (0) * dx, (-z1 + 1)/x^2 ) [] +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (x*z0) * dx, (-z0*z1 + z0)/x^2 ) [] +hol_form (x*z0) * dx +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (0) * dx, (-z0^2*z1 + z0^2 - z1^2)/x^2 ) [] +( (0) * dx, (-z0^2*z1 - z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Input In [73], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :83, in coordinates(self, threshold, basis) + +ValueError: I arrived at a form (omega, 0), in which omega is not regular on U0. I hoped this wouldn t happen. +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2).diffn()[?7h[?12l[?25h[?25l[?7l)/AS.x^2).expansion_at_nty()[?7h[?12l[?25h[?25l[?7l - AS.z[1]^2)/AS.x^2).dfn()[?7h[?12l[?25h[?25l[?7lsage: (((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2).diffn() +[?7h[?12l[?25h[?2004l[?7h((x^4*z0^2 - x^4*z1 + x^2*z0*z1 - z0^2*z1 - z1^2)/x^3) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage +┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.7, Release Date: 2022-09-19 │ +│ Using Python 3.10.5. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[ +RModule of dimension 1 over GF(3), +RModule of dimension 3 over GF(3), +RModule of dimension 6 over GF(3) +] +None +z1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (1) * dx, 0 ) [] +hol_form (1) * dx +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (z1) * dx, 0 ) [] +hol_form (z1) * dx +(z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx, 0 ) [] +hol_form (x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx +(x^2*z0 + z0^2*z1 + x^2 - z0*z1 + z1^2 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (z0 + 1) * dx, 0 ) [] +hol_form (z0 + 1) * dx +(z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (z0*z1 + z1) * dx, 0 ) [] +hol_form (z0*z1 + z1) * dx +(z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (z0^2 - z0 + 1) * dx, 0 ) [] +hol_form (z0^2 - z0 + 1) * dx +(z0^2 - z0 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (x) * dx, 0 ) [] +hol_form (x) * dx +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) [] +hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (x*z0 + x) * dx, 0 ) [] +hol_form (x*z0 + x) * dx +(x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (x^2) * dx, 0 ) [] +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (0) * dx, 0 ) [] +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (0) * dx, 0 ) [] +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-x^2) * dx, 0 ) [] +hol_form (-x^2) * dx +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-x^2 + z0*z1 - z1) * dx, 0 ) [] +hol_form (-x^2 + z0*z1 - z1) * dx +(-x^2 + z0*z1 - z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-x^2) * dx, 0 ) [] +hol_form (-x^2) * dx +(-x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-x^2*z0 - z0^2*z1 - z1^2) * dx, 0 ) [] +hol_form (-x^2*z0 - z0^2*z1 - z1^2) * dx +(-x^2*z0 - z0^2*z1 - z1^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-x*z0 + x) * dx, 0 ) [] +hol_form (-x*z0 + x) * dx +(-x*z0 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-x*z0^2 + x*z1) * dx, 0 ) [] +hol_form (-x*z0^2 + x*z1) * dx +(-x*z0^2 + x*z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-x*z0^2 + x*z0 + x*z1 - x) * dx, 0 ) [] +hol_form (-x*z0^2 + x*z0 + x*z1 - x) * dx +(-x*z0^2 + x*z0 + x*z1 - x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-z0*z1 + z1) * dx, (x^2*z1 - z0*z1^2 + z1^2)/x^3 ) [] +hol_form (-z0*z1 + z1) * dx +(-z0*z1 + z1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (1) * dx, 0 ) [] +hol_form (1) * dx +(1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (z1 + 1) * dx, 0 ) [] +hol_form (z1 + 1) * dx +(z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx, 0 ) [] +hol_form (x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx +(x^2*z0 + z0^2*z1 + z0^2 + z1^2 - z1 + 1) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (z0) * dx, 0 ) [] +hol_form (z0) * dx +(z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (z0*z1 + z0) * dx, 0 ) [] +hol_form (z0*z1 + z0) * dx +(z0*z1 + z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (z0^2) * dx, 0 ) [] +hol_form (z0^2) * dx +(z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (x) * dx, 0 ) [] +hol_form (x) * dx +(x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-x*z0^2 + x*z1 + x) * dx, 0 ) [] +hol_form (-x*z0^2 + x*z1 + x) * dx +(-x*z0^2 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (x*z0) * dx, 0 ) [] +hol_form (x*z0) * dx +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (x^2) * dx, 0 ) [] +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (0) * dx, 1/x ) [] +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (x^2) * dx, 1/x ) [] +hol_form (x^2) * dx +(x^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (0) * dx, z0/x ) [] +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (-z0^2) * dx, z0/x ) [] +hol_form (-z0^2) * dx +(-z0^2) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (0) * dx, (z0^2 - z1)/x ) [] +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (z0*z1 - z0) * dx, (z0^2 - z1)/x ) [] +hol_form (z0*z1 - z0) * dx +(z0*z1 - z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (0) * dx, (-z1 + 1)/x^2 ) [] +hol_form (0) * dx +(0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (x*z0) * dx, (-z0*z1 + z0)/x^2 ) [] +hol_form (x*z0) * dx +(x*z0) * dx [(1) * dx, (z1) * dx, (x^2*z0 + z0^2*z1 + z1^2) * dx, (z0) * dx, (z0*z1) * dx, (z0^2) * dx, (x) * dx, (-x*z0^2 + x*z1) * dx, (x*z0) * dx, (x^2) * dx] +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (0) * dx, (-z0^2*z1 + z0^2 - z1^2)/x^2 ) [] +( (0) * dx, (-z0^2*z1 - z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Input In [1], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :21, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :16, in  + +File :30, in group_action_matrices_dR(AS, threshold) + +File :9, in group_action_matrices(space, list_of_group_elements, basis) + +File :85, in coordinates(self, threshold, basis) + +ValueError: I arrived at a form (omega, 0), in which omega is not regular on U0. I hoped this wouldn t happen. +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAz0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7lSz0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-ASz0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1ASz0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l()ASz0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l()*ASz0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAz1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7lSz1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l.z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[] - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAz1^2)/x^2[?7h[?12l[?25h[?25l[?7lSz1^2)/x^2[?7h[?12l[?25h[?25l[?7l.z1^2)/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1^2)/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]^2)/x^2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lAx^2[?7h[?12l[?25h[?25l[?7lSx^2[?7h[?12l[?25h[?25l[?7l.x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l2.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: ((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2.expansion_at_infty() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Input In [2], in () +----> 1 ((-Integer(1))*AS.z[Integer(0)]**Integer(2)*AS.z[Integer(1)] - AS.z[Integer(1)]**Integer(2))/AS.x**Integer(2).expansion_at_infty() + +File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() + 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' + 493 """ +--> 494 return self.getattr_from_category(name) + 495 + 496 cdef getattr_from_category(self, name): + +File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() + 505 else: + 506 cls = P._abstract_element_class +--> 507 return getattr_from_other_class(self, cls, name) + 508 + 509 def __dir__(self): + +File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() + 359 dummy_error_message.cls = type(self) + 360 dummy_error_message.name = name +--> 361 raise AttributeError(dummy_error_message) + 362 attribute = attr + 363 # Check for a descriptor (__get__ in Python) + +AttributeError: 'sage.rings.integer.Integer' object has no attribute 'expansion_at_infty' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: ((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2 +[?7h[?12l[?25h[?2004l[?7h(-z0^2*z1 - z1^2)/x^2 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?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)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2.)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().diffn()[?7h[?12l[?25h[?25l[?7lexpasion_at_infty()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldiffn()[?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: (((-1)*AS.z[0]^2*AS.z[1] - 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AS.z[1]^2)/AS.x^2).diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l[- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l[]- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l[- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l()- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l(- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7lsage: ((- AS.z[1]^2)/AS.x^2).diffn() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [7], in () +----> 1 ((- AS.z[Integer(1)]**Integer(2))/AS.x**Integer(2)).diffn() + +TypeError: bad operand type for unary -: 'as_function' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((- AS.z[1]^2)/AS.x^2).diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(- AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1 AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l() AS.z[1]^2)/AS.x^2).difn()[?7h[?12l[?25h[?25l[?7l()* AS.z[1]^2)/AS.x^2).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[?7lsage: (((-1)* AS.z[1]^2)/AS.x^2).diffn() +[?7h[?12l[?25h[?2004l[?7h((-x^4*z1 - z1^2)/x^3) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(((-1)* AS.z[1]^2)/AS.x^2).diffn()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?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[?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[?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: (((-1)* AS.z[1]^2)/AS.x^2).valuation() +[?7h[?12l[?25h[?2004l[?7h-6 +[?2004h[?25l[?7lsage: [?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[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS +[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7lf(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l (-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l=(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l (-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7la(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7las(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7las_(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7lf(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7lu(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7ln(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7lc(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7lt(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7li(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7lo(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7ln(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l((-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7lA(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7lS(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l,(-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l (-z0^2*z1 - z1^2)/x^2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lxf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lyf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lzf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lQf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l,f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lRf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lxf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lyf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lzf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l,f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lxf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l,f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lyf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l,f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lzf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l=f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lAf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lSf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l.f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lcf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7ltf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l_f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lif = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lef = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7llf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7ldf = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l(f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l()f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l();f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: RxyzQ, Rxyz, x, y,z = AS.fct_field(); ff = as_function(AS, (-z0^2*z1 - z1^2)/x^2) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [12], in () +----> 1 RxyzQ, Rxyz, x, y,z = AS.fct_field(); ff = as_function(AS, (-z0**Integer(2)*z1 - z1**Integer(2))/x**Integer(2)) + +TypeError: 'tuple' object is not callable +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRxyzQ, Rxyz, x, y,z = AS.fct_field(); ff = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(; f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l; f = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lsage: RxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-z0^2*z1 - z1^2)/x^2) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Input In [13], in () +----> 1 RxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-z0**Integer(2)*z1 - z1**Integer(2))/x**Integer(2)) + +NameError: name 'z0' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[] - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1^2)/x^2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]^2)/x^2)[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*z[1] - z[1]^2)/x^2)[?7h[?12l[?25h[?25l[?7l3*z[1] - z[1]^2)/x^2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lz[1]^2)/x^2)[?7h[?12l[?25h[?25l[?7l[z[1]^2)/x^2)[?7h[?12l[?25h[?25l[?7l[]z[1]^2)/x^2)[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l0]z[1]^2)/x^2)[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[]*z[1]^2)/x^2)[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(x^2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l*))[?7h[?12l[?25h[?25l[?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[?7lsage: RxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-z[0]^3*z[1] - z[0]*z[1]^2)/(x^2*z[0])) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor eta in AS.de_rham_basis():[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ll[?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[?7lfor eta in AS.de_rham_basis():[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7las[?7h[?12l[?25h[?25l[?7las_[?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[?7lA[?7h[?12l[?25h[?25l[?7lS[?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[?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[?7lA[?7h[?12l[?25h[?25l[?7lS[?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[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: fff = as_cech(AS, as_form(AS, 0), ff) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff = as_cech(AS, as_form(AS, 0), ff)[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?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[?7lsage: fff. + fff.coordinates fff.group_action + fff.curve fff.omega0  + fff.f fff.omega8  + + [?7h[?12l[?25h[?25l[?7lcoordinates + fff.coordinates  + + + [?7h[?12l[?25h[?25l[?7l + + + +[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: fff.coordinates() +[?7h[?12l[?25h[?2004lz1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (0) * dx, (-z0^2*z1 - z1^2)/x^2 ) [] +( (0) * dx, (-z0^2*z1 - z1^2)/x^2 ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Input In [16], in () +----> 1 fff.coordinates() + +File :85, in coordinates(self, threshold, basis) + +ValueError: I arrived at a form (omega, 0), in which omega is not regular on U0. I hoped this wouldn t happen. +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff.coordinates()[?7h[?12l[?25h[?25l[?7l = as_cech(AS, as_form(AS, 0), ff)[?7h[?12l[?25h[?25l[?7lRxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-z[0]^3*z[1] - z[0]*z[1]^2)/(x^2*z[0]))[?7h[?12l[?25h[?25l[?7lfff = as_cech(AS, as_form(AS, 0), ff)[?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[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS +[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lfct_field[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lform[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lfff.coordinates()[?7h[?12l[?25h[?25l[?7l = as_cech(AS, as_form(AS, 0), ff)[?7h[?12l[?25h[?25l[?7lRxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-z[0]^3*z[1] - z[0]*z[1]^2)/(x^2*z[0]))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l(z[0]^3*z[1] - z[0]*z[1]^2)/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()*z[1] - z[0]*z[1]^2)/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l+)*z[1] - z[0]*z[1]^2)/(x^2*z[0])[?7h[?12l[?25h[?25l[?7lx)*z[1] - z[0]*z[1]^2)/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l^)*z[1] - z[0]*z[1]^2)/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l2)*z[1] - z[0]*z[1]^2)/(x^2*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+x^2)*z[1] - z[0]*z[1]^2)/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l[]+x^2)*z[1] - z[0]*z[1]^2)/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: RxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-(z[0]+x^2)*z[1] - z[0]*z[1]^2)/(x^2*z[0])) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-(z[0]+x^2)*z[1] - z[0]*z[1]^2)/(x^2*z[0]))[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lfff.coordinates()[?7h[?12l[?25h[?25l[?7l = as_cech(AS, as_form(AS, 0), ff)[?7h[?12l[?25h[?25l[?7lsage: fff = as_cech(AS, as_form(AS, 0), ff) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff = as_cech(AS, as_form(AS, 0), ff)[?7h[?12l[?25h[?25l[?7lRxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-(z[0]+x^2)*z[1] - z[0]*z[1]^2)/(x^2*z[0]))[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lfff.coordinates()[?7h[?12l[?25h[?25l[?7l = as_cech(AS, as_form(AS, 0), ff)[?7h[?12l[?25h[?25l[?7lRxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-z[0]^3*z[1] - z[0]*z[1]^2)/(x^2*z[0]))[?7h[?12l[?25h[?25l[?7l0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l(); ff= as_function(AS, (-z0^2*z1- z1^2)/x^2)[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l(((-1)* AS.z[1]^2)/AS.x^2).valuation()[?7h[?12l[?25h[?25l[?7ldiffn()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).diffn()[?7h[?12l[?25h[?25l[?7l(-1)*AS.z[0]^2*AS.z[1])/AS.x^2).valuation()[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1] - AS.z[1]^2)/AS.x^2).diffn()[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l(((-1)*AS.z[0]^2*AS.z[1])/AS.x^2).valuation()[?7h[?12l[?25h[?25l[?7l- AS.z[1]^2)/AS.x^2).diffn()[?7h[?12l[?25h[?25l[?7l(-1)* AS.z[1]^2)/AS.x^2).diffn()[?7h[?12l[?25h[?25l[?7lvaluation()[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lRxyzQ, Rxyz, x, y,z = AS.fct_field(); ff = as_function(AS, (-z0^2*z1 - z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l; ff =as_function(AS, (-z0^2*z1 -z1^2)/x^2)[?7h[?12l[?25h[?25l[?7l[0]^3*z[1] - z[0]*z[1]^2)/(x^2*z[0]))[?7h[?12l[?25h[?25l[?7lfff = as_cech(AS, as_form(AS, 0), ff)[?7h[?12l[?25h[?25l[?7lRxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-(z[0]+x^2)*z[1] - z[0]*z[1]^2)/(x^2*z[0]))[?7h[?12l[?25h[?25l[?7lfff = as_cech(AS, as_form(AS, 0), ff)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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 = as_cech(AS, as_form(AS, 0), ff)[?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[?2004lz1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (0) * dx, (-x^2*z1 - z0*z1^2 - z0*z1)/(x^2*z0) ) [] +( (0) * dx, (-x^2*z1 - z0*z1^2)/(x^2*z0) ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Input In [20], in () +----> 1 fff.coordinates() + +File :85, in coordinates(self, threshold, basis) + +ValueError: I arrived at a form (omega, 0), in which omega is not regular on U0. I hoped this wouldn t happen. +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff.coordinates()[?7h[?12l[?25h[?25l[?7l = as_cech(AS, as_form(AS, 0), ff)[?7h[?12l[?25h[?25l[?7lRxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-(z[0]+x^2)*z[1] - z[0]*z[1]^2)/(x^2*z[0]))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: RxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-(z[0]+x^2)*z[1] - z[0]*z[1]^2)/(x^2*z[0])) +[?7h[?12l[?25h[?2004l[?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[?7lsage: AS +[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations: +z0^3 - z0 = x^2 +z1^3 - z1 = x^4 + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lRxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-(z[0]+x^2)*z[1] - z[0]*z[1]^2)/(x^2*z[0]))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]^ - z[0]*z[1]^2)/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l2 - z[0]*z[1]^2)/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l)/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l)/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l)/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l)/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l)/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l(()/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l(())/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lz))/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l[))/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l]))/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l1])/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l+))/(x^2*z[0])[?7h[?12l[?25h[?25l[?7lx))/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l^))/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l4))/(x^2*z[0])[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l*))[?7h[?12l[?25h[?25l[?7lz))[?7h[?12l[?25h[?25l[?7l[))[?7h[?12l[?25h[?25l[?7l1))[?7h[?12l[?25h[?25l[?7l]))[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: RxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-(z[0]+x^2)*z[1]^2 - z[0]*(z[1]+x^4))/(x^2*z[0]*z[1])) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-(z[0]+x^2)*z[1]^2 - z[0]*(z[1]+x^4))/(x^2*z[0]*z[1]))[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lRxyzQ, Rxyz, x, y,z = AS.fct_field; ff = as_function(AS, (-(z[0]+x^2)*z[1] - z[0]*z[1]^2)/(x^2*z[0]))[?7h[?12l[?25h[?25l[?7lfff.coordinates()[?7h[?12l[?25h[?25l[?7l = as_cech(AS, as_form(AS, 0), ff)[?7h[?12l[?25h[?25l[?7lsage: fff = as_cech(AS, as_form(AS, 0), ff) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff = as_cech(AS, as_form(AS, 0), ff)[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7lsage: fff.coordinates() +[?7h[?12l[?25h[?2004lz1/x +z1^2/x +z0*z1/x +z0*z1^2/x +z0^2*z1/x +z0^2*z1^2/x +z1^2/x^2 +z0*z1^2/x^2 +z0^2*z1^2/x^2 +z0^2*z1^2/x^3 +[[0, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 0, 2, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2]] +( (0) * dx, (-x^4*z0 - x^2*z1^2 - z0*z1^2 - z0*z1)/(x^2*z0*z1) ) [] +( (0) * dx, (-x^2*z0 - z1^2)/(z0*z1) ) [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Input In [25], in () +----> 1 fff.coordinates() + +File :85, in coordinates(self, threshold, basis) + +ValueError: I arrived at a form (omega, 0), in which omega is not regular on U0. I hoped this wouldn t happen. +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h \ No newline at end of file diff --git a/sage/as_covers/as_cech_class.sage b/sage/as_covers/as_cech_class.sage index 5e286b7..04626c9 100644 --- a/sage/as_covers/as_cech_class.sage +++ b/sage/as_covers/as_cech_class.sage @@ -12,6 +12,9 @@ class as_cech: RxyzQ = FractionField(Rxyz) self.omega0 = omega self.f = f + self.omega8 = self.omega0 - self.f.diffn() + if self.omega0.form not in Rxyz or self.omega8.valuation() < 0: + raise ValueError('cech cocycle not regular') def __repr__(self): return "( " + str(self.omega0)+", " + str(self.f) + " )" @@ -41,6 +44,7 @@ class as_cech: def coordinates(self, threshold=10, basis = 0): '''Find coordinates of self in the de Rham cohomology basis. Threshold is an argument passed to AS.de_rham_basis().''' AS = self.curve + RxyzQ, Rxyz, x, y, z = AS.fct_field if basis == 0: basis = [AS.holomorphic_differentials_basis(), AS.cohomology_of_structure_sheaf_basis(), AS.de_rham_basis(threshold=threshold)] holo_diffs = basis[0] @@ -48,25 +52,37 @@ class as_cech: dR = basis[2] F = AS.base_ring f_products = [] - for i, f in enumerate(coh_basis): - f_products += [[]] - for omega in holo_diffs: - f_products[i] += [sum((f*omega).residue(place = _) for _ in range(AS.nb_of_pts_at_infty))] - + for f in coh_basis: + f_products += [[omega.serre_duality_pairing(f) for omega in holo_diffs]] + print(f_products) product_of_fct_and_omegas = [] fct = self.f - for omega in holo_diffs: - product_of_fct_and_omegas += [sum((fct*omega).residue(place = _) for _ in range(AS.nb_of_pts_at_infty))] + product_of_fct_and_omegas = [omega.serre_duality_pairing(fct) 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) #coeficients of self in the basis elts coming from cohomology of OX for i in range(AS.genus()): self -= coh_coordinates[i]*dR[i+AS.genus()] - - hol_form = self.omega0 + self.f.diffn() #now this should be a holomorphic form - hol_form = hol_form - print(hol_form) - return hol_form.coordinates() + coh_coordinates + #We remove now from f the summands which are obviously regular at infty + print(self, []) + f_num = numerator(self.f.function) + f_den = denominator(self.f.function) + v_f_den = as_function(AS, f_den).valuation() + for a in f_num.monomials(): + if as_function(AS, a).valuation() >= v_f_den: + self.f.function -= f_num.monomial_coefficient(a)*a/f_den + f_num = numerator(self.f.function) + f_den = denominator(self.f.function) + quo, rem = f_num.quo_rem(f_den) + if as_function(AS, rem/f_den).valuation() >= 0: + self.f = as_function(AS, quo) + hol_form = self.omega0 - self.f.diffn() #now this should be a holomorphic form + hol_form = as_form(AS, as_reduction(AS, hol_form.form)) + print('hol_form', hol_form) + return hol_form.coordinates() + coh_coordinates + print(self, [omega.serre_duality_pairing(self.f) for omega in holo_diffs]) + raise ValueError('I arrived at a form (omega, 0), in which omega is not regular on U0. I hoped this wouldn t happen.') + def group_action(self, g): AS = self.curve diff --git a/sage/as_covers/as_cover_class.sage b/sage/as_covers/as_cover_class.sage index 951c752..89b2a09 100644 --- a/sage/as_covers/as_cover_class.sage +++ b/sage/as_covers/as_cover_class.sage @@ -54,10 +54,10 @@ class as_cover: all_z_series += [z_series] all_dx_series += [x_series.derivative()] self.jumps = all_jumps - self.x = all_x_series - self.y = all_y_series - self.z = all_z_series - self.dx = all_dx_series + self.x_series = all_x_series + self.y_series = all_y_series + self.z_series = all_z_series + self.dx_series = all_dx_series ############## #Function field variable_names = 'x, y' @@ -68,6 +68,11 @@ class as_cover: z = Rxyz.gens()[2:] RxyzQ = FractionField(Rxyz) self.fct_field = (RxyzQ, Rxyz, x, y, z) + self.x = as_function(self, x) + self.y = as_function(self, y) + self.z = [as_function(self, z[i]) for i in range(n)] + self.dx = as_form(self, 1) + def __repr__(self): n = self.height @@ -104,10 +109,10 @@ class as_cover: def holomorphic_differentials_basis(self, threshold = 8): from itertools import product - x_series = self.x - y_series = self.y - z_series = self.z - dx_series = self.dx + x_series = self.x_series + y_series = self.y_series + z_series = self.z_series + dx_series = self.dx_series delta = self.nb_of_pts_at_infty p = self.characteristic n = self.height @@ -145,9 +150,9 @@ class as_cover: """ Find fcts with pole order in infty's at most pole_order. Threshold gives a bound on powers of x in the function. If you suspect that you haven't found all the functions, you may increase it.""" from itertools import product - x_series = self.x - y_series = self.y - z_series = self.z + x_series = self.x_series + y_series = self.y_series + z_series = self.z_series delta = self.nb_of_pts_at_infty p = self.characteristic n = self.height @@ -197,9 +202,9 @@ class as_cover: """Find forms with pole order in all the points at infty equat at most to pole_order. Threshold gives a bound on powers of x in the form. If you suspect that you haven't found all the functions, you may increase it.""" from itertools import product - x_series = self.x - y_series = self.y - z_series = self.z + x_series = self.x_series + y_series = self.y_series + z_series = self.z_series delta = self.nb_of_pts_at_infty p = self.characteristic n = self.height @@ -297,9 +302,9 @@ class as_cover: def cohomology_of_structure_sheaf_basis(self, threshold = 8): holo_diffs = self.holomorphic_differentials_basis(threshold = threshold) from itertools import product - x_series = self.x - y_series = self.y - z_series = self.z + x_series = self.x_series + y_series = self.y_series + z_series = self.z_series delta = self.nb_of_pts_at_infty p = self.characteristic n = self.height @@ -321,9 +326,7 @@ class as_cover: for j in range(0, m): for k in product(*pr): f = as_function(self, prod(z[i1]^(k[i1]) for i1 in range(n))/x^i*y^j) - f_products = [] - for omega in holo_diffs: - f_products += [sum((f*omega).residue(place = _) for _ in range(self.nb_of_pts_at_infty))] + f_products = [omega.serre_duality_pairing(f) for omega in holo_diffs] if vector(f_products) not in S: S = S+V.subspace([V(f_products)]) result_fcts += [f] @@ -334,10 +337,10 @@ class as_cover: '''Given function fct, find form eta regular on affine part such that eta - d(fct) is regular in infty. (Works for one place at infty now)''' print(fct) from itertools import product - x_series = self.x - y_series = self.y - z_series = self.z - dx_series = self.dx + x_series = self.x_series + y_series = self.y_series + z_series = self.z_series + dx_series = self.dx_series delta = self.nb_of_pts_at_infty p = self.characteristic n = self.height @@ -363,8 +366,8 @@ class as_cover: raise ValueError("Increase threshold!") for omega in forms: for a in F: - if (a*omega - fct.diffn()).form in Rxyz: - return a*omega + if (a*omega + fct.diffn()).form in Rxyz: + return a*omega + fct.diffn() raise ValueError("Unknown.") def de_rham_basis(self, threshold = 30): diff --git a/sage/as_covers/as_form_class.sage b/sage/as_covers/as_form_class.sage index 43c094c..303d5ed 100644 --- a/sage/as_covers/as_form_class.sage +++ b/sage/as_covers/as_form_class.sage @@ -19,10 +19,10 @@ class as_form: C = self.curve delta = C.nb_of_pts_at_infty F = C.base_ring - x_series = C.x[i] - y_series = C.y[i] - z_series = C.z[i] - dx_series = C.dx[i] + x_series = C.x_series[i] + y_series = C.y_series[i] + z_series = C.z_series[i] + dx_series = C.dx_series[i] n = C.height variable_names = 'x, y' for j in range(n): @@ -57,14 +57,7 @@ class as_form: def group_action(self, ZN_tuple): C = self.curve n = C.height - F = C.base_ring - 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:] - RxyzQ = FractionField(Rxyz) + RxyzQ, Rxyz, x, y, z = C.fct_field sub_list = {x : x, y : y} | {z[j] : z[j]+ZN_tuple[j] for j in range(n)} g = self.form return as_form(C, g.substitute(sub_list)) @@ -80,6 +73,7 @@ class as_form: denom = LCM([denominator(omega.form) for omega in basis]) basis = [denom*omega for omega in basis] self_with_no_denominator = denom*self + print(self_with_no_denominator, basis) return linear_representation_polynomials(Rxyz(self_with_no_denominator.form), [Rxyz(omega.form) for omega in basis]) def trace(self): @@ -110,6 +104,10 @@ class as_form: def valuation(self, place=0): return self.expansion_at_infty(i = place).valuation() + def serre_duality_pairing(self, fct): + AS = self.curve + return sum((fct*self).residue(place = _) for _ in range(AS.nb_of_pts_at_infty)) + def artin_schreier_transform(power_series, prec = 10): """Given a power_series, find correction such that power_series - (correction)^p +correction has valuation -jump non divisible by p. Also, express t (the variable) in terms of the uniformizer at infty on the curve diff --git a/sage/as_covers/as_function_class.sage b/sage/as_covers/as_function_class.sage index b80f30e..696115c 100644 --- a/sage/as_covers/as_function_class.sage +++ b/sage/as_covers/as_function_class.sage @@ -60,9 +60,9 @@ class as_function: C = self.curve delta = C.nb_of_pts_at_infty F = C.base_ring - x_series = C.x[i] - y_series = C.y[i] - z_series = C.z[i] + x_series = C.x_series[i] + y_series = C.y_series[i] + z_series = C.z_series[i] n = C.height variable_names = 'x, y' for j in range(n):