Easy fix at https://trac.sagemath.org/ticket/34653, please review!
Martin
On Thursday, 13 October 2022 at 00:05:37 UTC+2 Martin R wrote:
> OK, I think now I am down to what's quite clearly a bug:
>
> sage: P.<x,y> = PolynomialRing(SR)
> sage: R.<z> = PolynomialRing(P, sparse=False); R
> Univariate Polynomial Ring in z over Multivariate Polynomial Ring in x, y
> over Symbolic Ring
> sage: A = -x*z^2 + x*z
> sage: B = -x
> sage: A // B
> z^2 - z
> sage: P.<x,y> = PolynomialRing(SR)
> sage: R.<z> = PolynomialRing(P, sparse=True); R
> Sparse Univariate Polynomial Ring in z over Multivariate Polynomial Ring
> in x, y over Symbolic Ring
> sage: A = -x*z^2 + x*z
> sage: B = -x
> sage: A // B
> ---------------------------------------------------------------------------
> TypeError Traceback (most recent call last)
> File
> ~/sage-develop/src/sage/rings/polynomial/polynomial_element_generic.py:852,
> in Polynomial_generic_sparse.quo_rem(self, other)
> 851 try:
> --> 852 c = R(rem.leading_coefficient() * ~other.leading_coefficient())
> 853 except TypeError:
>
> File ~/sage-develop/src/sage/structure/parent.pyx:897, in
> sage.structure.parent.Parent.__call__()
> 896 if no_extra_args:
> --> 897 return mor._call_(x)
> 898 else:
>
> File ~/sage-develop/src/sage/structure/coerce_maps.pyx:161, in
> sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
> 160 print(type(C._element_constructor), C._element_constructor)
> --> 161 raise
> 162
>
> File ~/sage-develop/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 ~/sage-develop/src/sage/rings/polynomial/polynomial_ring.py:456, in
> PolynomialRing_general._element_constructor_(self, x, check, is_gen,
> construct, **kwds)
> 455 else:
> --> 456 raise TypeError("denominator must be a unit")
> 457 elif isinstance(x, pari_gen):
>
> TypeError: denominator must be a unit
>
> During handling of the above exception, another exception occurred:
>
> ArithmeticError Traceback (most recent call last)
> Input In [39], in <cell line: 1>()
> ----> 1 A // B
>
> File ~/sage-develop/src/sage/structure/element.pyx:1840, in
> sage.structure.element.Element.__floordiv__()
> 1838 return (<Element>left)._floordiv_(right)
> 1839 if BOTH_ARE_ELEMENT(cl):
> -> 1840 return coercion_model.bin_op(left, right, floordiv)
> 1841
> 1842 try:
>
> File ~/sage-develop/src/sage/structure/coerce.pyx:1204, in
> sage.structure.coerce.CoercionModel.bin_op()
> 1202 self._record_exception()
> 1203 else:
> -> 1204 return PyObject_CallObject(op, xy)
> 1205
> 1206 if op is mul:
>
> File ~/sage-develop/src/sage/structure/element.pyx:1838, in
> sage.structure.element.Element.__floordiv__()
> 1836 cdef int cl = classify_elements(left, right)
> 1837 if HAVE_SAME_PARENT(cl):
> -> 1838 return (<Element>left)._floordiv_(right)
> 1839 if BOTH_ARE_ELEMENT(cl):
> 1840 return coercion_model.bin_op(left, right, floordiv)
>
> File ~/sage-develop/src/sage/rings/polynomial/polynomial_element.pyx:2872,
> in sage.rings.polynomial.polynomial_element.Polynomial._floordiv_()
> 2870 # quite typical when removing gcds...
> 2871 return self
> -> 2872 Q, _ = self.quo_rem(right)
> 2873 return Q
> 2874
>
> File ~/sage-develop/src/sage/structure/element.pyx:4498, in
> sage.structure.element.coerce_binop.new_method()
> 4496 def new_method(self, other, *args, **kwargs):
> 4497 if have_same_parent(self, other):
> -> 4498 return method(self, other, *args, **kwargs)
> 4499 else:
> 4500 a, b = coercion_model.canonical_coercion(self, other)
>
> File
> ~/sage-develop/src/sage/rings/polynomial/polynomial_element_generic.py:854,
> in Polynomial_generic_sparse.quo_rem(self, other)
> 852 c = R(rem.leading_coefficient() * ~other.leading_coefficient())
> 853 except TypeError:
> --> 854 raise ArithmeticError("Division non exact (consider coercing
> to polynomials over the fraction field)")
> 855 e = rem.degree() - d
> 856 quo += c*R.one().shift(e)
>
> ArithmeticError: Division non exact (consider coercing to polynomials over
> the fraction field)
> sage:
>
> On Wednesday, 12 October 2022 at 23:50:04 UTC+2 Martin R wrote:
>
>> Possibly related:
>>
>> sage: P.<x,y> = PolynomialRing(SR)
>> sage: R.<z> = PolynomialRing(P); R
>> Univariate Polynomial Ring in z over Multivariate Polynomial Ring in x, y
>> over Symbolic Ring
>> sage: num = -x*z^2 + x*z
>> sage: den = x*z^2 + (-x-1)*z + 1
>> sage: num.gcd(den)
>> z - 1
>> sage: P.<x,y> = PolynomialRing(SR)
>> sage: R.<z> = PolynomialRing(P, sparse=True); R
>> Sparse Univariate Polynomial Ring in z over Multivariate Polynomial Ring
>> in x, y over Symbolic Ring
>> sage: num = -x*z^2 + x*z
>> sage: den = x*z^2 + (-x-1)*z + 1
>> sage: num.gcd(den)
>>
>>
>> ---------------------------------------------------------------------------
>> TypeError Traceback (most recent call
>> last)
>> File
>> ~/sage-develop/src/sage/rings/polynomial/polynomial_element_generic.py:852,
>> in Polynomial_generic_sparse.quo_rem(self, other)
>> 851 try:
>> --> 852 c = R(rem.leading_coefficient() *
>> ~other.leading_coefficient())
>> 853 except TypeError:
>>
>>
>> File ~/sage-develop/src/sage/structure/parent.pyx:897, in
>> sage.structure.parent.Parent.__call__()
>> 896 if no_extra_args:
>> --> 897 return mor._call_(x)
>> 898 else:
>>
>> File ~/sage-develop/src/sage/structure/coerce_maps.pyx:161, in
>> sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
>> 160 print(type(C._element_constructor), C._element_constructor)
>> --> 161 raise
>> 162
>>
>> File ~/sage-develop/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 ~/sage-develop/src/sage/rings/polynomial/polynomial_ring.py:456, in
>> PolynomialRing_general._element_constructor_(self, x, check, is_gen,
>> construct, **kwds)
>> 455 else:
>> --> 456 raise TypeError("denominator must be a unit")
>> 457 elif isinstance(x, pari_gen):
>>
>> TypeError: denominator must be a unit
>>
>>
>> During handling of the above exception, another exception occurred:
>>
>> ArithmeticError Traceback (most recent call
>> last)
>> Input In [82], in <cell line: 1>()
>> ----> 1 num.gcd(den)
>>
>>
>> File ~/sage-develop/src/sage/structure/element.pyx:4498, in
>> sage.structure.element.coerce_binop.new_method()
>> 4496 def new_method(self, other, *args, **kwargs):
>> 4497 if have_same_parent(self, other):
>> -> 4498 return method(self, other, *args, **kwargs)
>> 4499 else:
>> 4500 a, b = coercion_model.canonical_coercion(self, other)
>>
>> File
>> ~/sage-develop/src/sage/rings/polynomial/polynomial_element_generic.py:935,
>> in Polynomial_generic_sparse.gcd(self, other, algorithm)
>> 933 return S(g)
>> 934 elif algorithm=="generic":
>> --> 935 return Polynomial.gcd(self,other)
>> 936 else:
>> 937 raise ValueError("Unknown algorithm '%s'" % algorithm)
>>
>>
>> File ~/sage-develop/src/sage/structure/element.pyx:4498, in
>> sage.structure.element.coerce_binop.new_method()
>> 4496 def new_method(self, other, *args, **kwargs):
>> 4497 if have_same_parent(self, other):
>> -> 4498 return method(self, other, *args, **kwargs)
>> 4499 else:
>> 4500 a, b = coercion_model.canonical_coercion(self, other)
>>
>> File
>> ~/sage-develop/src/sage/rings/polynomial/polynomial_element.pyx:4918, in
>> sage.rings.polynomial.polynomial_element.Polynomial.gcd()
>> 4916 raise NotImplementedError("%s does not provide a gcd
>> implementation for univariate polynomials"%self._parent._base)
>> 4917 else:
>> -> 4918 return doit(self, other)
>> 4919
>> 4920 @coerce_binop
>>
>> File
>> ~/sage-develop/src/sage/categories/unique_factorization_domains.py:185, in
>> UniqueFactorizationDomains.ParentMethods._gcd_univariate_polynomial(self,
>> f, g)
>> 182 break
>> 184 d = a.gcd(b)
>> --> 185 A = A // a
>> 186 B = B // b
>> 187 g = h = 1
>>
>> File ~/sage-develop/src/sage/structure/element.pyx:1840, in
>> sage.structure.element.Element.__floordiv__()
>> 1838 return (<Element>left)._floordiv_(right)
>> 1839 if BOTH_ARE_ELEMENT(cl):
>> -> 1840 return coercion_model.bin_op(left, right, floordiv)
>> 1841
>> 1842 try:
>>
>> File ~/sage-develop/src/sage/structure/coerce.pyx:1204, in
>> sage.structure.coerce.CoercionModel.bin_op()
>> 1202 self._record_exception()
>> 1203 else:
>> -> 1204 return PyObject_CallObject(op, xy)
>> 1205
>> 1206 if op is mul:
>>
>> File ~/sage-develop/src/sage/structure/element.pyx:1838, in
>> sage.structure.element.Element.__floordiv__()
>> 1836 cdef int cl = classify_elements(left, right)
>> 1837 if HAVE_SAME_PARENT(cl):
>> -> 1838 return (<Element>left)._floordiv_(right)
>> 1839 if BOTH_ARE_ELEMENT(cl):
>> 1840 return coercion_model.bin_op(left, right, floordiv)
>>
>> File
>> ~/sage-develop/src/sage/rings/polynomial/polynomial_element.pyx:2872, in
>> sage.rings.polynomial.polynomial_element.Polynomial._floordiv_()
>> 2870 # quite typical when removing gcds...
>> 2871 return self
>> -> 2872 Q, _ = self.quo_rem(right)
>> 2873 return Q
>> 2874
>>
>> File ~/sage-develop/src/sage/structure/element.pyx:4498, in
>> sage.structure.element.coerce_binop.new_method()
>> 4496 def new_method(self, other, *args, **kwargs):
>> 4497 if have_same_parent(self, other):
>> -> 4498 return method(self, other, *args, **kwargs)
>> 4499 else:
>> 4500 a, b = coercion_model.canonical_coercion(self, other)
>>
>> File
>> ~/sage-develop/src/sage/rings/polynomial/polynomial_element_generic.py:854,
>> in Polynomial_generic_sparse.quo_rem(self, other)
>> 852 c = R(rem.leading_coefficient() *
>> ~other.leading_coefficient())
>> 853 except TypeError:
>> --> 854 raise ArithmeticError("Division non exact (consider coercing
>> to polynomials over the fraction field)")
>> 855 e = rem.degree() - d
>> 856 quo += c*R.one().shift(e)
>>
>> ArithmeticError: Division non exact (consider coercing to polynomials
>> over the fraction field)
>>
>> On Wednesday, 12 October 2022 at 22:39:46 UTC+2 Martin R wrote:
>>
>>> I am not sure whether the following is to be expected.
>>>
>>> Martin
>>>
>>> sage: R.<x> = SR[]
>>> sage: S.<z> = R[]
>>> sage: (x*z).quo_rem(S(x))
>>>
>>> ---------------------------------------------------------------------------
>>> TypeError Traceback (most recent call
>>> last)
>>> File
>>> ~/sage-develop/src/sage/rings/polynomial/polynomial_element.pyx:11713, in
>>> sage.rings.polynomial.polynomial_element.Polynomial_generic_dense.quo_rem()
>>> 11712 try:
>>> > 11713 q = R(q)
>>> 11714 except TypeError:
>>>
>>> File ~/sage-develop/src/sage/structure/parent.pyx:897, in
>>> sage.structure.parent.Parent.__call__()
>>> 896 if no_extra_args:
>>> --> 897 return mor._call_(x)
>>> 898 else:
>>>
>>> File ~/sage-develop/src/sage/categories/map.pyx:788, in
>>> sage.categories.map.Map._call_()
>>> 787
>>> --> 788 cpdef Element _call_(self, x):
>>> 789 """
>>>
>>> File ~/sage-develop/src/sage/rings/fraction_field.py:1254, in
>>> FractionFieldEmbeddingSection._call_(self, x, check)
>>> 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
>>>
>>> During handling of the above exception, another exception occurred:
>>>
>>> ArithmeticError Traceback (most recent call
>>> last)
>>> Input In [41], in <cell line: 1>()
>>> ----> 1 (x*z).quo_rem(S(x))
>>>
>>> File ~/sage-develop/src/sage/structure/element.pyx:4498, in
>>> sage.structure.element.coerce_binop.new_method()
>>> 4496 def new_method(self, other, *args, **kwargs):
>>> 4497 if have_same_parent(self, other):
>>> -> 4498 return method(self, other, *args, **kwargs)
>>> 4499 else:
>>> 4500 a, b = coercion_model.canonical_coercion(self, other)
>>>
>>> File
>>> ~/sage-develop/src/sage/rings/polynomial/polynomial_element.pyx:11715, in
>>> sage.rings.polynomial.polynomial_element.Polynomial_generic_dense.quo_rem()
>>> 11713 q = R(q)
>>> 11714 except TypeError:
>>> > 11715 raise ArithmeticError("division non exact (consider coercing
>>> to polynomials over the fraction field)")
>>> 11716 for j from n+k-2 >= j >= k:
>>> 11717 x[j] -= q * y[j-k]
>>>
>>> ArithmeticError: division non exact (consider coercing to polynomials
>>> over the fraction field)
>>> sage:
>>
>>
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