usuniete zbedne komunikaty

sage/.run.term-0.term

@@ -34265,4 +34265,607 @@ A.diffn().is_regular_on_U0() True
 [0] d[x] + [0] d[y] + V((2*a*x^21 + 2*x^15 + (a + 1)*x^13 + 2*a*x^12) dy) + dV(0)
 [?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lf[1][?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lF.cardinality()[?7h[?12l[?25h[?25l[?7lanth_root(p)[?7h[?12l[?25h[?25l[?7lomega.carier()[?7h[?12l[?25h[?25l[?7l = a*omega[?7h[?12l[?25h[?25l[?7l.cartier()[?7h[?12l[?25h[?25l[?7l = (C.x)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lmult_by_p(fct.diffn()) == (fct^p).verschiebung().diffn()[?7h[?12l[?25h[?25l[?7lfct = C.y[?7h[?12l[?25h[?25l[?7lC =superelliptic(x^3 - x, m)[?7h[?12l[?25h[?25l[?7lfct= C.y[?7h[?12l[?25h[?25l[?7lsage: fct = C.y
 [?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfct = C.y[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lf[1][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lfct = C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmult_by_p(fct.diffn()) == (fct^p).verschiebung().diffn()[?7h[?12l[?25h[?25l[?7lsage: mult_by_p(fct.diffn()) == (fct^p).verschiebung().diffn()
-[?7h[?12l[?25h[?2004l
+[?7h[?12l[?25h[?2004l[?7hTrue
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit()
+[?7h[?12l[?25h[?2004l]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ cd ..
+]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add -u
+]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git commit -m "naprawioney brak (1/p)-liniowosci cartiera)"
+[master 1f66cae] naprawiony brak (1/p)-liniowosci cartiera
+ 6 files changed, 2428 insertions(+), 13 deletions(-)
+]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git push
+Username for 'https://git.wmi.amu.edu.pl': jgarnek
+Password for 'https://jgarnek@git.wmi.amu.edu.pl': 
+Enumerating objects: 23, done.
+Counting objects:   4% (1/23)
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Counting objects: 100% (23/23)
Counting objects: 100% (23/23), done.
+Delta compression using up to 4 threads
+Compressing objects:   8% (1/12)
Compressing objects:  16% (2/12)
Compressing objects:  25% (3/12)
Compressing objects:  33% (4/12)
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Compressing objects: 100% (12/12), done.
+Writing objects:   8% (1/12)
Writing objects:  16% (2/12)
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Writing objects: 100% (12/12), 14.29 KiB | 232.00 KiB/s, done.
+Total 12 (delta 11), reused 0 (delta 0)
+remote: . Processing 1 references
+remote: Processed 1 references in total
+To https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git
+   a5c2ce2..1f66cae  master -> master
+]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ scd sage
+]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
+┌────────────────────────────────────────────────────────────────────┐
+│ SageMath version 9.8, Release Date: 2023-02-11                     │
+│ Create a "Sage Worksheet" file for the notebook interface.         │
+│ Enhanced for CoCalc.                                               │
+│ Using Python 3.11.1. Type "help()" for help.                       │
+└────────────────────────────────────────────────────────────────────┘
+]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
+[?7h[?12l[?25h[?2004lTrue
+[0] d[x] + [0] d[y] + V((2*a*x^9 + 2*x^3 + (a + 1)*x + 2*a) dy) + dV(0)
+True
+[0] d[x] + [0] d[y] + V((2*a*x^12 + 2*x^6 + (a + 1)*x^4 + 2*a*x^3) dy) + dV(0)
+True
+[0] d[x] + [0] d[y] + V((2*a*x^15 + 2*x^9 + (a + 1)*x^7 + 2*a*x^6) dy) + dV(0)
+True
+^C---------------------------------------------------------------------------
+KeyboardInterrupt                         Traceback (most recent call last)
+File <string>:59, in __mul__(self, other)
+
+File <string>:260, in reduction(C, g)
+
+File /ext/sage/9.8/src/sage/arith/misc.py:2021, in xgcd(a, b)
+   2020 try:
+-> 2021     return a.xgcd(b)
+   2022 except AttributeError:
+
+File /ext/sage/9.8/src/sage/structure/element.pyx:4497, in sage.structure.element.coerce_binop.new_method()
+   4496 if have_same_parent(self, other):
+-> 4497     return method(self, other, *args, **kwargs)
+   4498 else:
+
+File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_element.pyx:8931, in sage.rings.polynomial.polynomial_element.Polynomial.xgcd()
+   8930 if hasattr(self.base_ring(), '_xgcd_univariate_polynomial'):
+-> 8931     return self.base_ring()._xgcd_univariate_polynomial(self, other)
+   8932 else:
+
+File /ext/sage/9.8/src/sage/categories/fields.py:373, in Fields.ParentMethods._xgcd_univariate_polynomial(self, a, b)
+    372 while v3:
+--> 373     q, r = d.quo_rem(v3)
+    374     (u, d, v1, v3) = (v1, v3, u - v1*q, r)
+
+File /ext/sage/9.8/src/sage/structure/element.pyx:4497, in sage.structure.element.coerce_binop.new_method()
+   4496 if have_same_parent(self, other):
+-> 4497     return method(self, other, *args, **kwargs)
+   4498 else:
+
+File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_element.pyx:11734, in sage.rings.polynomial.polynomial_element.Polynomial_generic_dense.quo_rem()
+  11733 for k from m-n >= k >= 0:
+> 11734     q = x[n+k-1] * inv
+  11735     for j from n+k-2 >= j >= k:
+
+File /ext/sage/9.8/src/sage/structure/element.pyx:1513, in sage.structure.element.Element.__mul__()
+   1512 if HAVE_SAME_PARENT(cl):
+-> 1513     return (<Element>left)._mul_(right)
+   1514 if BOTH_ARE_ELEMENT(cl):
+
+File /ext/sage/9.8/src/sage/rings/fraction_field_element.pyx:670, in sage.rings.fraction_field_element.FractionFieldElement._mul_()
+    669 d2 = snum.gcd(rden)
+--> 670 if not d1.is_unit():
+    671     rnum = rnum // d1
+
+File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_element.pyx:5544, in sage.rings.polynomial.polynomial_element.Polynomial.is_unit()
+   5543     return self._parent._base.zero().is_unit()
+-> 5544 return self.get_unsafe(0).is_unit()
+   5545 
+
+File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_zz_pex.pyx:180, in sage.rings.polynomial.polynomial_zz_pex.Polynomial_ZZ_pEX.get_unsafe()
+    179 cdef ZZ_pE_c c_pE = ZZ_pEX_coeff(self.x, i)
+--> 180 return self._parent._base(ZZ_pE_c_to_list(c_pE))
+    181 
+
+File /ext/sage/9.8/src/sage/structure/parent.pyx:896, in sage.structure.parent.Parent.__call__()
+    895 if no_extra_args:
+--> 896     return mor._call_(x)
+    897 else:
+
+File /ext/sage/9.8/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+
+File /ext/sage/9.8/src/sage/rings/finite_rings/finite_field_givaro.py:230, in FiniteField_givaro._element_constructor_(self, e)
+    228     return self._cache.random_element()
+--> 230 def _element_constructor_(self, e):
+    231     """
+    232     Coerces several data types to ``self``.
+    233 
+   (...)
+    369         2*a4^3 + 2*a4^2 + 1
+    370     """
+
+File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
+
+KeyboardInterrupt: 
+
+During handling of the above exception, another exception occurred:
+
+AttributeError                            Traceback (most recent call last)
+Cell In [1], line 1
+----> 1 load('init.sage')
+
+File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:32
+
+File /ext/sage/9.8/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.8/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:30
+
+File <string>:82, in regular_drw_form(omega)
+
+File <string>:99, in diffn(self, dy_w)
+
+File <string>:73, in diffn(self, dy_w)
+
+File <string>:177, in dy_w(C)
+
+File <string>:149, in auxilliary_derivative(P)
+
+File <string>:55, in __rmul__(self, other)
+
+File /ext/sage/9.8/src/sage/rings/integer.pyx:1961, in sage.rings.integer.Integer.__mul__()
+   1959         return y
+   1960 
+-> 1961     return coercion_model.bin_op(left, right, operator.mul)
+   1962 
+   1963 cpdef _mul_(self, right):
+
+File /ext/sage/9.8/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
+   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
+   1241 if mul_method is not None:
+-> 1242     res = mul_method(x)
+   1243     if res is not None and res is not NotImplemented:
+   1244         return res
+
+File <string>:55, in __rmul__(self, other)
+
+File /ext/sage/9.8/src/sage/rings/integer.pyx:1961, in sage.rings.integer.Integer.__mul__()
+   1959         return y
+   1960 
+-> 1961     return coercion_model.bin_op(left, right, operator.mul)
+   1962 
+   1963 cpdef _mul_(self, right):
+
+File /ext/sage/9.8/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
+   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
+   1241 if mul_method is not None:
+-> 1242     res = mul_method(x)
+   1243     if res is not None and res is not NotImplemented:
+   1244         return res
+
+File <string>:55, in __rmul__(self, other)
+
+File /ext/sage/9.8/src/sage/rings/integer.pyx:1961, in sage.rings.integer.Integer.__mul__()
+   1959         return y
+   1960 
+-> 1961     return coercion_model.bin_op(left, right, operator.mul)
+   1962 
+   1963 cpdef _mul_(self, right):
+
+File /ext/sage/9.8/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
+   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
+   1241 if mul_method is not None:
+-> 1242     res = mul_method(x)
+   1243     if res is not None and res is not NotImplemented:
+   1244         return res
+
+File <string>:55, in __rmul__(self, other)
+
+File <string>:84, in __add__(self, other)
+
+File <string>:65, in __mul__(self, other)
+
+File <string>:63, in __mul__(self, other)
+
+AttributeError: 'superelliptic_function' object has no attribute 'form'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for b in C1.de_rham_basis():
+....:     print(mult_by_p(b.omega0).regular_form())[?7h[?12l[?25h[?25l[?7l....:     print(mult_by_p(b.omega0).regular_form())
+....: [?7h[?12l[?25h[?25l[?7lsage: for b in C1.de_rham_basis():
+....:     print(mult_by_p(b.omega0).regular_form())
+....: 
+[?7h[?12l[?25h[?2004l^C---------------------------------------------------------------------------
+KeyboardInterrupt                         Traceback (most recent call last)
+Cell In [2], line 1
+----> 1 for b in C1.de_rham_basis():
+      2     print(mult_by_p(b.omega0).regular_form())
+
+File <string>:123, in de_rham_basis(self)
+
+File <string>:105, in basis_de_rham_degrees(self)
+
+File <string>:5, in __init__(self, C, omega, fct)
+
+File <string>:28, in __sub__(self, other)
+
+File <string>:7, in __init__(self, C, g)
+
+File <string>:296, in reduction_form(C, g)
+
+File /ext/sage/9.8/src/sage/structure/element.pyx:1515, in sage.structure.element.Element.__mul__()
+   1513     return (<Element>left)._mul_(right)
+   1514 if BOTH_ARE_ELEMENT(cl):
+-> 1515     return coercion_model.bin_op(left, right, mul)
+   1516 
+   1517 cdef long value
+
+File /ext/sage/9.8/src/sage/structure/coerce.pyx:1200, in sage.structure.coerce.CoercionModel.bin_op()
+   1198 # Now coerce to a common parent and do the operation there
+   1199 try:
+-> 1200     xy = self.canonical_coercion(x, y)
+   1201 except TypeError:
+   1202     self._record_exception()
+
+File /ext/sage/9.8/src/sage/structure/coerce.pyx:1315, in sage.structure.coerce.CoercionModel.canonical_coercion()
+   1313     x_elt = x
+   1314 if y_map is not None:
+-> 1315     y_elt = (<Map>y_map)._call_(y)
+   1316 else:
+   1317     y_elt = y
+
+File /ext/sage/9.8/src/sage/structure/coerce_maps.pyx:432, in sage.structure.coerce_maps.CallableConvertMap._call_()
+    430         y = self._func(C, x)
+    431     else:
+--> 432         y = self._func(x)
+    433 except Exception:
+    434     if print_warnings:
+
+File /ext/sage/9.8/src/sage/rings/fraction_field.py:324, in FractionField_generic._coerce_map_from_.<locals>.wrapper(x)
+    323 def wrapper(x):
+--> 324     return self._element_class(self, x.numerator(), x.denominator())
+
+File /ext/sage/9.8/src/sage/rings/fraction_field_element.pyx:1167, in sage.rings.fraction_field_element.FractionFieldElement_1poly_field.__init__()
+   1165     1/2/x
+   1166 """
+-> 1167 FractionFieldElement.__init__(self, parent, numerator, denominator,
+   1168         coerce, reduce)
+   1169 if not reduce:
+
+File /ext/sage/9.8/src/sage/rings/fraction_field_element.pyx:121, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
+    119 if reduce and parent.is_exact():
+    120     try:
+--> 121         self.reduce()
+    122     except ArithmeticError:
+    123         pass
+
+File /ext/sage/9.8/src/sage/rings/fraction_field_element.pyx:1239, in sage.rings.fraction_field_element.FractionFieldElement_1poly_field.reduce()
+   1237 if self._is_reduced:
+   1238     return
+-> 1239 super(self.__class__, self).reduce()
+   1240 self.normalize_leading_coefficients()
+   1241 
+
+File /ext/sage/9.8/src/sage/rings/fraction_field_element.pyx:164, in sage.rings.fraction_field_element.FractionFieldElement.reduce()
+    162     return codomain.coerce(nnum/nden)
+    163 
+--> 164 cpdef reduce(self):
+    165     """
+    166     Reduce this fraction.
+
+File /ext/sage/9.8/src/sage/rings/fraction_field_element.pyx:210, in sage.rings.fraction_field_element.FractionFieldElement.reduce()
+    208 if not self.__denominator.is_one() and self.__denominator.is_unit():
+    209     try:
+--> 210         inv = self.__denominator.inverse_of_unit()
+    211     except Exception:
+    212         pass
+
+File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_element.pyx:1524, in sage.rings.polynomial.polynomial_element.Polynomial.inverse_of_unit()
+   1522 else:
+   1523     cst = self.get_unsafe(0)
+-> 1524 inv = cst.inverse_of_unit()
+   1525 return self._parent([inv])
+   1526 
+
+File /ext/sage/9.8/src/sage/categories/fields.py:817, in Fields.ElementMethods.inverse_of_unit(self)
+    787 def inverse_of_unit(self):
+    788     r"""
+    789     Return the inverse of this element.
+    790 
+   (...)
+    815         +infinity
+    816     """
+--> 817     return ~self
+
+File /ext/sage/9.8/src/sage/rings/fraction_field_element.pyx:934, in sage.rings.fraction_field_element.FractionFieldElement.__invert__()
+    932 if self.is_zero():
+    933     raise ZeroDivisionError("Cannot invert 0")
+--> 934 return self.__class__(self._parent,
+    935     self.__denominator, self.__numerator, coerce=False, reduce=False)
+    936 
+
+File /ext/sage/9.8/src/sage/rings/fraction_field_element.pyx:1170, in sage.rings.fraction_field_element.FractionFieldElement_1poly_field.__init__()
+   1168             coerce, reduce)
+   1169     if not reduce:
+-> 1170         self.normalize_leading_coefficients()
+   1171 
+   1172 cdef normalize_leading_coefficients(self):
+
+File /ext/sage/9.8/src/sage/rings/fraction_field_element.pyx:1177, in sage.rings.fraction_field_element.FractionFieldElement_1poly_field.normalize_leading_coefficients()
+   1175 """
+   1176 invlc = ~self.__denominator.leading_coefficient()
+-> 1177 self.__denominator = self.__denominator.monic()
+   1178 self.__numerator *= invlc
+   1179 
+
+File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_element.pyx:5724, in sage.rings.polynomial.polynomial_element.Polynomial.monic()
+   5722 - Naqi Jaffery (2006-01-24): examples
+   5723 """
+-> 5724 if self.is_monic():
+   5725     return self
+   5726 a = ~self.leading_coefficient()
+
+File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_element.pyx:5497, in sage.rings.polynomial.polynomial_element.Polynomial.is_monic()
+   5495     - Naqi Jaffery (2006-01-24): examples
+   5496     """
+-> 5497     return not self.is_zero() and self[self.degree()] == 1
+   5498 
+   5499 def is_unit(self):
+
+File /ext/sage/9.8/src/sage/structure/element.pyx:1111, in sage.structure.element.Element.__richcmp__()
+   1109         return (<Element>self)._richcmp_(other, op)
+   1110     else:
+-> 1111         return coercion_model.richcmp(self, other, op)
+   1112 
+   1113 cpdef _richcmp_(left, right, int op):
+
+File /ext/sage/9.8/src/sage/structure/coerce.pyx:1973, in sage.structure.coerce.CoercionModel.richcmp()
+   1971 # Coerce to a common parent
+   1972 try:
+-> 1973     x, y = self.canonical_coercion(x, y)
+   1974 except (TypeError, NotImplementedError):
+   1975     pass
+
+File /ext/sage/9.8/src/sage/structure/coerce.pyx:1315, in sage.structure.coerce.CoercionModel.canonical_coercion()
+   1313     x_elt = x
+   1314 if y_map is not None:
+-> 1315     y_elt = (<Map>y_map)._call_(y)
+   1316 else:
+   1317     y_elt = y
+
+File /ext/sage/9.8/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.8/src/sage/rings/finite_rings/finite_field_givaro.py:230, in FiniteField_givaro._element_constructor_(self, e)
+    212     """
+    213     Return a random element of ``self``.
+    214 
+   (...)
+    226         True
+    227     """
+    228     return self._cache.random_element()
+--> 230 def _element_constructor_(self, e):
+    231     """
+    232     Coerces several data types to ``self``.
+    233 
+   (...)
+    369         2*a4^3 + 2*a4^2 + 1
+    370     """
+    371     return self._cache.element_from_data(e)
+
+File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
+
+KeyboardInterrupt: 
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for b in C1.de_rham_basis():
+....:     print(mult_by_p(b.omega0).regular_form())[?7h[?12l[?25h[?25l[?7l....:     print(mult_by_p(b.omega0).regular_form())
+....: [?7h[?12l[?25h[?25l[?7lsage: for b in C1.de_rham_basis():
+....:     print(mult_by_p(b.omega0).regular_form())
+....: 
+[?7h[?12l[?25h[?2004lTrue
+[0] d[x] + [0] d[y] + V((2*a*x^9 + 2*x^3 + (a + 1)*x + 2*a) dy) + dV(0)
+True
+^C---------------------------------------------------------------------------
+KeyboardInterrupt                         Traceback (most recent call last)
+Cell In [3], line 2
+      1 for b in C1.de_rham_basis():
+----> 2     print(mult_by_p(b.omega0).regular_form())
+
+File <string>:82, in regular_drw_form(omega)
+
+File <string>:73, in diffn(self, dy_w)
+
+File <string>:177, in dy_w(C)
+
+File <string>:149, in auxilliary_derivative(P)
+
+File <string>:149, in auxilliary_derivative(P)
+
+File <string>:149, in auxilliary_derivative(P)
+
+File <string>:147, in auxilliary_derivative(P)
+
+File <string>:35, in __sub__(self, other)
+
+File <string>:32, in __add__(self, other)
+
+File <string>:39, in __add__(self, other)
+
+File <string>:260, in reduction(C, g)
+
+File /ext/sage/9.8/src/sage/arith/misc.py:2021, in xgcd(a, b)
+   1933 r"""
+   1934 Return a triple ``(g,s,t)`` such that `g = s\cdot a+t\cdot b = \gcd(a,b)`.
+   1935 
+   (...)
+   2018     (1, 7*a^2/b^2, (((-h)*a)/b^2)*y + 1/b)
+   2019 """
+   2020 try:
+-> 2021     return a.xgcd(b)
+   2022 except AttributeError:
+   2023     a = py_scalar_to_element(a)
+
+File /ext/sage/9.8/src/sage/structure/element.pyx:4497, in sage.structure.element.coerce_binop.new_method()
+   4495 def new_method(self, other, *args, **kwargs):
+   4496     if have_same_parent(self, other):
+-> 4497         return method(self, other, *args, **kwargs)
+   4498     else:
+   4499         a, b = coercion_model.canonical_coercion(self, other)
+
+File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_element.pyx:8931, in sage.rings.polynomial.polynomial_element.Polynomial.xgcd()
+   8929 """
+   8930 if hasattr(self.base_ring(), '_xgcd_univariate_polynomial'):
+-> 8931     return self.base_ring()._xgcd_univariate_polynomial(self, other)
+   8932 else:
+   8933     raise NotImplementedError("%s does not provide an xgcd implementation for univariate polynomials"%self.base_ring())
+
+File /ext/sage/9.8/src/sage/categories/fields.py:378, in Fields.ParentMethods._xgcd_univariate_polynomial(self, a, b)
+    376 if d:
+    377     c = ~d.leading_coefficient()
+--> 378     d, u, v = c*d, c*u, c*v
+    379 return d, u, v
+
+File /ext/sage/9.8/src/sage/structure/element.pyx:1515, in sage.structure.element.Element.__mul__()
+   1513     return (<Element>left)._mul_(right)
+   1514 if BOTH_ARE_ELEMENT(cl):
+-> 1515     return coercion_model.bin_op(left, right, mul)
+   1516 
+   1517 cdef long value
+
+File /ext/sage/9.8/src/sage/structure/coerce.pyx:1194, in sage.structure.coerce.CoercionModel.bin_op()
+   1192 if action is not None:
+   1193     if (<Action>action)._is_left:
+-> 1194         return (<Action>action)._act_(x, y)
+   1195     else:
+   1196         return (<Action>action)._act_(y, x)
+
+File /ext/sage/9.8/src/sage/structure/coerce_actions.pyx:612, in sage.structure.coerce_actions.LeftModuleAction._act_()
+    610 if self.extended_base is not None:
+    611     a = <ModuleElement?>self.extended_base(a)
+--> 612 return (<ModuleElement>a)._rmul_(<Element>g)  # g * a
+    613 
+    614 
+
+File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_element.pyx:11518, in sage.rings.polynomial.polynomial_element.Polynomial_generic_dense._rmul_()
+  11516 if c._parent is not (<Element>self.__coeffs[0])._parent:
+  11517     c = (<Element>self.__coeffs[0])._parent.coerce(c)
+> 11518 v = [c * a for a in self.__coeffs]
+  11519 cdef Polynomial_generic_dense res = self._new_c(v, self._parent)
+  11520 #if not v[len(v)-1]:
+
+File /ext/sage/9.8/src/sage/structure/element.pyx:1513, in sage.structure.element.Element.__mul__()
+   1511 cdef int cl = classify_elements(left, right)
+   1512 if HAVE_SAME_PARENT(cl):
+-> 1513     return (<Element>left)._mul_(right)
+   1514 if BOTH_ARE_ELEMENT(cl):
+   1515     return coercion_model.bin_op(left, right, mul)
+
+File /ext/sage/9.8/src/sage/rings/fraction_field_element.pyx:686, in sage.rings.fraction_field_element.FractionFieldElement._mul_()
+    684         except NotImplementedError:
+    685             pass
+--> 686     return self.__class__(self._parent, tnum, tden,
+    687         coerce=False, reduce=False)
+    688 except AttributeError:
+
+File /ext/sage/9.8/src/sage/rings/fraction_field_element.pyx:1170, in sage.rings.fraction_field_element.FractionFieldElement_1poly_field.__init__()
+   1168             coerce, reduce)
+   1169     if not reduce:
+-> 1170         self.normalize_leading_coefficients()
+   1171 
+   1172 cdef normalize_leading_coefficients(self):
+
+File /ext/sage/9.8/src/sage/rings/fraction_field_element.pyx:1178, in sage.rings.fraction_field_element.FractionFieldElement_1poly_field.normalize_leading_coefficients()
+   1176     invlc = ~self.__denominator.leading_coefficient()
+   1177     self.__denominator = self.__denominator.monic()
+-> 1178     self.__numerator *= invlc
+   1179 
+   1180 def is_integral(self):
+
+File /ext/sage/9.8/src/sage/structure/element.pyx:1515, in sage.structure.element.Element.__mul__()
+   1513     return (<Element>left)._mul_(right)
+   1514 if BOTH_ARE_ELEMENT(cl):
+-> 1515     return coercion_model.bin_op(left, right, mul)
+   1516 
+   1517 cdef long value
+
+File /ext/sage/9.8/src/sage/structure/coerce.pyx:1196, in sage.structure.coerce.CoercionModel.bin_op()
+   1194         return (<Action>action)._act_(x, y)
+   1195     else:
+-> 1196         return (<Action>action)._act_(y, x)
+   1197 
+   1198 # Now coerce to a common parent and do the operation there
+
+File /ext/sage/9.8/src/sage/structure/coerce_actions.pyx:645, in sage.structure.coerce_actions.RightModuleAction._act_()
+    643 if self.extended_base is not None:
+    644     a = <ModuleElement?>self.extended_base(a)
+--> 645 return (<ModuleElement>a)._lmul_(<Element>g)  # a * g
+    646 
+    647 
+
+File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_zz_pex.pyx:221, in sage.rings.polynomial.polynomial_zz_pex.Polynomial_ZZ_pEX._lmul_()
+    219 r._parent = (<Polynomial_template>self)._parent
+    220 r._cparent = (<Polynomial_template>self)._cparent
+--> 221 d = self._parent._modulus.ZZ_pE(list(left.polynomial()))
+    222 ZZ_pEX_mul_ZZ_pE(r.x, self.x, d.x)
+    223 return r
+
+File /ext/sage/9.8/src/sage/libs/ntl/ntl_ZZ_pEContext.pyx:154, in sage.libs.ntl.ntl_ZZ_pEContext.ntl_ZZ_pEContext_class.ZZ_pE()
+    152     """
+    153     from .ntl_ZZ_pE import ntl_ZZ_pE
+--> 154     return ntl_ZZ_pE(v,modulus=self)
+    155 
+    156 def ZZ_pEX(self, v = None):
+
+File /ext/sage/9.8/src/sage/libs/ntl/ntl_ZZ_pE.pyx:117, in sage.libs.ntl.ntl_ZZ_pE.ntl_ZZ_pE.__init__()
+    115     self.x = ZZ_pX_to_ZZ_pE((<ntl_ZZ_pX>v).x)
+    116 elif isinstance(v, (list, tuple)):
+--> 117     tmp_zzpx = <ntl_ZZ_pX>ntl_ZZ_pX(v, self.c.pc)
+    118     self.c.restore_c()   # allocating tmp_zzpx can change the current modulus trac #25790
+    119     self.x = ZZ_pX_to_ZZ_pE(tmp_zzpx.x)
+
+File /ext/sage/9.8/src/sage/libs/ntl/ntl_ZZ_pX.pyx:108, in sage.libs.ntl.ntl_ZZ_pX.ntl_ZZ_pX.__init__()
+    106 for i, x in enumerate(v):
+    107     if not isinstance(x, ntl_ZZ_p):
+--> 108         cc = ntl_ZZ_p(x, self.c)
+    109         self.c.restore_c()
+    110     else:
+
+File /ext/sage/9.8/src/sage/libs/ntl/ntl_ZZ_p.pyx:131, in sage.libs.ntl.ntl_ZZ_p.ntl_ZZ_p.__init__()
+    129     ZZ_p_div(self.x, ZZ_to_ZZ_p(num), ZZ_to_ZZ_p(den))
+    130 else:
+--> 131     str_v = str(v)  # can cause modulus to change  trac #25790
+    132     self.c.restore_c()
+    133     ccreadstr(self.x, str_v)
+
+File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
+
+KeyboardInterrupt: 
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
+[?7h[?12l[?25h[?2004l[0] d[x] + [0] d[y] + V((2*a*x^9 + 2*x^3 + (a + 1)*x + 2*a) dy) + dV(0)
+[0] d[x] + [0] d[y] + V((2*a*x^12 + 2*x^6 + (a + 1)*x^4 + 2*a*x^3) dy) + dV(0)
+[0] d[x] + [0] d[y] + V((2*a*x^15 + 2*x^9 + (a + 1)*x^7 + 2*a*x^6) dy) + dV(0)
+[0] d[x] + [0] d[y] + V((2*a*x^18 + 2*x^12 + (a + 1)*x^10 + 2*a*x^9) dy) + dV(0)
+[0] d[x] + [0] d[y] + V((2*a*x^30 + 2*x^24 + (a + 1)*x^22 + 2*a*x^21 + (a + 1)*x^12 + a*x^6 + (a + 2)*x^4 + (a + 1)*x^3) dy) + dV(0)
+[0] d[x] + [0] d[y] + V((a*x^27 + x^21 + (2*a + 2)*x^19 + a*x^18 + (2*a + 2)*x^9 + 2*a*x^3 + (2*a + 1)*x + 2*a + 2) dy) + dV(0)
+[0] d[x] + [0] d[y] + V((0) dy) + dV(0)
+[0] d[x] + [0] d[y] + V((2*a*x^21 + 2*x^15 + (a + 1)*x^13 + 2*a*x^12) dy) + dV(0)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h

sage/superelliptic_drw/regular_form.sage

@@ -73,22 +73,15 @@ class superelliptic_regular_drw_form:
         return "[" + str(self.dx) + "] d[x] + [" + str(self.dy) + "] d[y] + V(" + str(self.omega) + ") + dV(" + str(self.h2) + ")"
         
 def regular_drw_form(omega):
-    print(omega.frobenius().is_regular_on_U0())
     C = omega.curve
     p = C.characteristic
     omega_aux = omega.r()
     omega_aux = omega_aux.regular_form()
     aux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn()
-    print("aux == omega", aux == omega)
     aux1 = aux.omega
     aux.omega, fct = decomposition_omega0_hpdh(aux.omega)
-    print('aux.omega, fct', aux.omega, fct, aux1.cartier() == fct.diffn(), aux1.verschiebung() == mult_by_p(fct.diffn()))
-    print('mult_by_p(fct.diffn()) == (fct^p).verschiebung().diffn()', mult_by_p(fct.diffn()) == (fct^p).verschiebung().diffn())
     aux.h2 += fct^p
-    print(aux.omega.is_regular_on_U0(), aux.frobenius().is_regular_on_U0())
-    print('aux - omega', aux - omega)
     aux.h2, A = decomposition_g0_pth_power(aux.h2)
-    print('A.diffn().is_regular_on_U0()', A.diffn().is_regular_on_U0())
     aux.omega += (A.diffn()).inv_cartier()
     result = superelliptic_regular_drw_form(omega_aux.dx, omega_aux.dy, aux.omega.regular_form(), aux.h2)
     return result