from sage.rings.polynomial.infinite_polynomial_element import
InfinitePolynomial_dense
is my friend!
On Wednesday, 22 November 2023 at 11:40:12 UTC+1 Martin R wrote:
> I need the variables of a polynomial c in InfinitePolynomialRing(SR) as an
> element of that ring (rather than as an element of the PolynomialRing).
>
> I understand that polynomials are hard, but does anybody see a workaround?
>
> Martin
>
> sage: R.<a> = InfinitePolynomialRing(SR)
> sage: c = 3*a[0]
> sage: c.variables()[0].parent()
> Multivariate Polynomial Ring in a_1, a_0 over Symbolic Ring
> sage: R(c.variables()[0])
> ---------------------------------------------------------------------------
> RuntimeError Traceback (most recent call last)
> Cell In [9], line 1
> ----> 1 R(c.variables()[Integer(0)])
>
> File ~/sage/src/sage/structure/parent.pyx:901, in
> sage.structure.parent.Parent.__call__()
> 899 if mor is not None:
> 900 if no_extra_args:
> --> 901 return mor._call_(x)
> 902 else:
> 903 return mor._call_with_args(x, args, kwds)
>
> File ~/sage/src/sage/structure/coerce_maps.pyx:163, in
> sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
> 161 print(type(C), C)
> 162 print(type(C._element_constructor),
> C._element_constructor)
> --> 163 raise
> 164
> 165 cpdef Element _call_with_args(self, x, args=(), kwds={}) noexcept:
>
> File ~/sage/src/sage/structure/coerce_maps.pyx:158, in
> sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
> 156 cdef Parent C = self._codomain
> 157 try:
> --> 158 return C._element_constructor(x)
> 159 except Exception:
> 160 if print_warnings:
>
> File ~/sage/src/sage/rings/polynomial/infinite_polynomial_ring.py:988, in
> InfinitePolynomialRing_sparse._element_constructor_(self, x)
> 985 # By now, x or self._P are not libsingular. Since
> MPolynomialRing_polydict
> 986 # is too buggy, we use string evaluation
> 987 try:
> --> 988 return sage_eval(repr(x), self.gens_dict())
> 989 except (ValueError, TypeError, NameError):
> 990 raise ValueError("cannot convert %s into an element of %s - no
> conversion into underlying polynomial ring" % (x, self))
>
> File ~/sage/src/sage/misc/cachefunc.pyx:2329, in
> sage.misc.cachefunc.CachedMethodCallerNoArgs.__call__()
> 2327 if self.cache is None:
> 2328 f = self.f
> -> 2329 self.cache = f(self._instance)
> 2330 return self.cache
> 2331
>
> File ~/sage/src/sage/rings/polynomial/infinite_polynomial_ring.py:1278, in
> InfinitePolynomialRing_sparse.gens_dict(self)
> 1263 @cached_method
> 1264 def gens_dict(self):
> 1265 """
> 1266 Return a dictionary-like object containing the infinitely many
> 1267 ``{var_name:variable}`` pairs.
> (...)
> 1276 a_5
> 1277 """
> -> 1278 return GenDictWithBasering(self, InfiniteGenDict(self.gens()))
>
> File ~/sage/src/sage/rings/polynomial/infinite_polynomial_ring.py:560, in
> GenDictWithBasering.__init__(self, parent, start)
> 558 while hasattr(P, 'base_ring') and (P.base_ring() is not P):
> 559 P = P.base_ring()
> --> 560 D = P.gens_dict()
> 561 if isinstance(D, GenDictWithBasering):
> 562 self._D.extend(D._D)
>
> File ~/sage/src/sage/structure/category_object.pyx:287, in
> sage.structure.category_object.CategoryObject.gens_dict()
> 285 """
> 286 if copy:
> --> 287 return dict(self.__gens_dict())
> 288 else:
> 289 return self.__gens_dict()
>
> File ~/sage/src/sage/misc/cachefunc.pyx:2329, in
> sage.misc.cachefunc.CachedMethodCallerNoArgs.__call__()
> 2327 if self.cache is None:
> 2328 f = self.f
> -> 2329 self.cache = f(self._instance)
> 2330 return self.cache
> 2331
>
> File ~/sage/src/sage/structure/category_object.pyx:261, in
> sage.structure.category_object.CategoryObject._CategoryObject__gens_dict()
> 259 def __gens_dict(self):
> 260 cdef dict v = {}
> --> 261 for x in self._defining_names():
> 262 v[str(x)] = x
> 263 return v
>
> File ~/sage/src/sage/misc/cachefunc.pyx:2329, in
> sage.misc.cachefunc.CachedMethodCallerNoArgs.__call__()
> 2327 if self.cache is None:
> 2328 f = self.f
> -> 2329 self.cache = f(self._instance)
> 2330 return self.cache
> 2331
>
> File ~/sage/src/sage/structure/category_object.pyx:407, in
> sage.structure.category_object.CategoryObject._defining_names()
> 405 ((1/2, 0, 0), (0, 1, 0))
> 406 """
> --> 407 return self.gens()
> 408
> 409
> #################################################################################################
>
> File ~/sage/src/sage/structure/parent_gens.pyx:119, in
> sage.structure.parent_gens.ParentWithGens.gens()
> 117 if self._gens is not None:
> 118 return self._gens
> --> 119 self._gens = tuple(self.gen(i) for i in range(self.ngens()))
> 120 return self._gens
> 121
>
> File ~/sage/src/sage/structure/parent_gens.pyx:103, in
> sage.structure.parent_gens.ParentWithGens.ngens()
> 101 # Derived class *must* define ngens method.
> 102 def ngens(self):
> --> 103 check_old_coerce(self)
> 104 raise NotImplementedError("Number of generators not known.")
> 105
>
> File ~/sage/src/sage/structure/parent_gens.pyx:78, in
> sage.structure.parent_gens.check_old_coerce()
> 76 cdef inline check_old_coerce(parent.Parent p) noexcept:
> 77 if p._element_constructor is not None:
> ---> 78 raise RuntimeError("%s still using old coercion framework"
> % p)
> 79
> 80
>
> RuntimeError: Symbolic Ring still using old coercion framework
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