def _coerce_map_from_(self, R):
r"""
Return a coerce map from ``R`` to this field.
EXAMPLES::
sage: R.<t> = GF(5)[]
sage: K = R.fraction_field()
sage: L = K.function_field()
sage: f = K.coerce_map_from(L); f # indirect doctest
Isomorphism:
From: Rational function field in t over Finite Field of size 5
To: Fraction Field of Univariate Polynomial Ring in t over Finite Field of size 5
sage: f(~L.gen())
1/t
"""
from sage.rings.function_field.function_field import is_RationalFunctionField
if is_RationalFunctionField(R) and self.variable_name(
) == R.variable_name() and self.base_ring() is R.constant_base_field():
from sage.categories.all import Hom
parent = Hom(R, self)
from sage.rings.function_field.maps import FunctionFieldToFractionField
return parent.__make_element_class__(FunctionFieldToFractionField)(
parent)
return super(FractionField_1poly_field, self)._coerce_map_from_(R)
def _coerce_map_from_(self, R):
r"""
Return a coerce map from ``R`` to this field.
EXAMPLES::
sage: R.<t> = GF(5)[]
sage: K = R.fraction_field()
sage: L = K.function_field()
sage: f = K.coerce_map_from(L); f # indirect doctest
Isomorphism:
From: Rational function field in t over Finite Field of size 5
To: Fraction Field of Univariate Polynomial Ring in t over Finite Field of size 5
sage: f(~L.gen())
1/t
"""
from sage.rings.function_field.function_field import is_RationalFunctionField
if is_RationalFunctionField(R) and self.variable_name() == R.variable_name() and self.base_ring() is R.constant_base_field():
from sage.categories.all import Hom
parent = Hom(R, self)
from sage.rings.function_field.maps import FunctionFieldToFractionField
return parent.__make_element_class__(FunctionFieldToFractionField)(parent)
return super(FractionField_1poly_field, self)._coerce_map_from_(R)
def can_convert_to_singular(R):
"""
Returns True if this ring's base field or ring can be
represented in Singular, and the polynomial ring has at
least one generator. If this is True then this polynomial
ring can be represented in Singular.
The following base rings are supported: finite fields, rationals, number
fields, and real and complex fields.
EXAMPLES::
sage: from sage.rings.polynomial.polynomial_singular_interface import can_convert_to_singular
sage: can_convert_to_singular(PolynomialRing(QQ, names=['x']))
True
sage: can_convert_to_singular(PolynomialRing(ZZ, names=['x']))
True
sage: can_convert_to_singular(PolynomialRing(QQ, names=[]))
False
TESTS:
Avoid non absolute number fields (see :trac:`23535`)::
sage: K.<a,b> = NumberField([x^2-2,x^2-5])
sage: can_convert_to_singular(K['s,t'])
False
"""
if R.ngens() == 0:
return False
base_ring = R.base_ring()
if (base_ring is ZZ
or sage.rings.finite_rings.finite_field_constructor.is_FiniteField(
base_ring) or is_RationalField(base_ring)
or is_IntegerModRing(base_ring) or is_RealField(base_ring)
or is_ComplexField(base_ring) or is_RealDoubleField(base_ring)
or is_ComplexDoubleField(base_ring)):
return True
elif base_ring.is_prime_field():
return base_ring.characteristic() <= 2147483647
elif number_field.number_field_base.is_NumberField(base_ring):
return base_ring.is_absolute()
elif sage.rings.fraction_field.is_FractionField(base_ring):
B = base_ring.base_ring()
return B.is_prime_field() or B is ZZ or is_FiniteField(B)
elif is_RationalFunctionField(base_ring):
return base_ring.constant_field().is_prime_field()
else:
return False
def can_convert_to_singular(R):
"""
Returns True if this ring's base field or ring can be
represented in Singular, and the polynomial ring has at
least one generator. If this is True then this polynomial
ring can be represented in Singular.
The following base rings are supported: finite fields, rationals, number
fields, and real and complex fields.
EXAMPLES::
sage: from sage.rings.polynomial.polynomial_singular_interface import can_convert_to_singular
sage: can_convert_to_singular(PolynomialRing(QQ, names=['x']))
True
sage: can_convert_to_singular(PolynomialRing(QQ, names=[]))
False
TESTS:
Avoid non absolute number fields (see :trac:`23535`)::
sage: K.<a,b> = NumberField([x^2-2,x^2-5])
sage: can_convert_to_singular(K['s,t'])
False
"""
if R.ngens() == 0:
return False;
base_ring = R.base_ring()
if (base_ring is ZZ
or sage.rings.finite_rings.finite_field_constructor.is_FiniteField(base_ring)
or is_RationalField(base_ring)
or is_IntegerModRing(base_ring)
or is_RealField(base_ring)
or is_ComplexField(base_ring)
or is_RealDoubleField(base_ring)
or is_ComplexDoubleField(base_ring)):
return True
elif base_ring.is_prime_field():
return base_ring.characteristic() <= 2147483647
elif number_field.number_field_base.is_NumberField(base_ring):
return base_ring.is_absolute()
elif sage.rings.fraction_field.is_FractionField(base_ring):
B = base_ring.base_ring()
return B.is_prime_field() or B is ZZ or is_FiniteField(B)
elif is_RationalFunctionField(base_ring):
return base_ring.constant_field().is_prime_field()
else:
return False
def can_convert_to_singular(R):
"""
Returns True if this ring's base field or ring can be
represented in Singular, and the polynomial ring has at
least one generator. If this is True then this polynomial
ring can be represented in Singular.
The following base rings are supported: finite fields, rationals, number
fields, and real and complex fields.
EXAMPLES::
sage: from sage.rings.polynomial.polynomial_singular_interface import can_convert_to_singular
sage: can_convert_to_singular(PolynomialRing(QQ, names=['x']))
True
sage: can_convert_to_singular(PolynomialRing(QQ, names=[]))
False
"""
if R.ngens() == 0:
return False
base_ring = R.base_ring()
return (
sage.rings.finite_rings.constructor.is_FiniteField(base_ring)
or is_RationalField(base_ring)
or (base_ring.is_prime_field()
and base_ring.characteristic() <= 2147483647)
or is_RealField(base_ring) or is_ComplexField(base_ring)
or is_RealDoubleField(base_ring) or is_ComplexDoubleField(base_ring)
or number_field.number_field_base.is_NumberField(base_ring) or
(sage.rings.fraction_field.is_FractionField(base_ring) and
(base_ring.base_ring().is_prime_field() or base_ring.base_ring() is ZZ
or is_FiniteField(base_ring.base_ring()))) or base_ring is ZZ
or is_IntegerModRing(base_ring)
or (is_RationalFunctionField(base_ring)
and base_ring.constant_field().is_prime_field()))
def can_convert_to_singular(R):
"""
Returns True if this ring's base field or ring can be
represented in Singular, and the polynomial ring has at
least one generator. If this is True then this polynomial
ring can be represented in Singular.
The following base rings are supported: finite fields, rationals, number
fields, and real and complex fields.
EXAMPLES::
sage: from sage.rings.polynomial.polynomial_singular_interface import can_convert_to_singular
sage: can_convert_to_singular(PolynomialRing(QQ, names=['x']))
True
sage: can_convert_to_singular(PolynomialRing(QQ, names=[]))
False
"""
if R.ngens() == 0:
return False;
base_ring = R.base_ring()
return ( sage.rings.finite_rings.constructor.is_FiniteField(base_ring)
or is_RationalField(base_ring)
or (base_ring.is_prime_field() and base_ring.characteristic() <= 2147483647)
or is_RealField(base_ring)
or is_ComplexField(base_ring)
or is_RealDoubleField(base_ring)
or is_ComplexDoubleField(base_ring)
or number_field.number_field_base.is_NumberField(base_ring)
or ( sage.rings.fraction_field.is_FractionField(base_ring) and ( base_ring.base_ring().is_prime_field() or base_ring.base_ring() is ZZ or is_FiniteField(base_ring.base_ring()) ) )
or base_ring is ZZ
or is_IntegerModRing(base_ring)
or (is_RationalFunctionField(base_ring) and base_ring.constant_field().is_prime_field()) )