def _coerce_map_from_(self, other):
"""
TESTS::
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import *
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_module import *
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_element import *
sage: from psage.modform.fourier_expansion_framework.gradedexpansions.gradedexpansion_grading import DegreeGrading
sage: from psage.modform.fourier_expansion_framework.gradedexpansions.gradedexpansion_module import *
sage: m = FreeModule(QQ, 3)
sage: mpsm = MonoidPowerSeriesModule(m, NNMonoid(False))
sage: mps = mpsm.base_ring()
sage: ger = GradedExpansionModule_class(Sequence([MonoidPowerSeries(mps, {1: 1}, mps.monoid().filter(4))]), Sequence([MonoidPowerSeries(mpsm, {1: m([1,1,1]), 2: m([1,3,-3])}, mpsm.monoid().filter(4))]), PolynomialRing(QQ, ['a', 'b']).ideal(0), DegreeGrading((1,2)))
sage: ger._coerce_map_from_(ZZ)
"""
if other is self.relations().ring():
from sage.structure.coerce_maps import CallableConvertMap
return CallableConvertMap(other, self, self._element_constructor_)
if isinstance(other, GradedExpansionSubmodule_abstract):
if other.graded_ambient() is self \
or self.has_coerce_map_from(other.graded_ambient()) :
from sage.structure.coerce_maps import CallableConvertMap
return CallableConvertMap(
other, self,
other._graded_expansion_submodule_to_graded_ambient_)
return Module._coerce_map_from_(self, other)
def _coerce_map_from_(self, R):
"""
EXAMPLES::
sage: L.<x,y> = LaurentPolynomialRing(QQ)
sage: L.coerce_map_from(QQ)
Composite map:
From: Rational Field
To: Multivariate Laurent Polynomial Ring in x, y over Rational Field
Defn: Polynomial base injection morphism:
From: Rational Field
To: Multivariate Polynomial Ring in x, y over Rational Field
then
Call morphism:
From: Multivariate Polynomial Ring in x, y over Rational Field
To: Multivariate Laurent Polynomial Ring in x, y over Rational Field
"""
if R is self._R:
from sage.structure.coerce_maps import CallableConvertMap
return CallableConvertMap(R,
self,
self._element_constructor_,
parent_as_first_arg=False)
else:
f = self._R.coerce_map_from(R)
if f is not None:
from sage.categories.homset import Hom
from sage.categories.morphism import CallMorphism
return CallMorphism(Hom(self._R, self)) * f
def _coerce_map_from_(self, S):
"""
Return a coerce map from ``S``.
EXAMPLES::
sage: f = QQ.coerce_map_from(ZZ); f # indirect doctest
Natural morphism:
From: Integer Ring
To: Rational Field
sage: f(3)
3
sage: f(3^99) - 3^99
0
sage: f = QQ.coerce_map_from(int); f # indirect doctest
Native morphism:
From: Set of Python objects of class 'int'
To: Rational Field
sage: f(44)
44
::
sage: QQ.coerce_map_from(long) # indirect doctest py2
Native morphism:
From: Set of Python objects of class 'long'
To: Rational Field
::
sage: L = Localization(ZZ, (3,5))
sage: 1/45 in L # indirect doctest
True
sage: 1/43 in L # indirect doctest
False
"""
global ZZ
from . import rational
if ZZ is None:
from . import integer_ring
ZZ = integer_ring.ZZ
if S is ZZ:
return rational.Z_to_Q()
elif S is _long_type:
return rational.long_to_Q()
elif S is int:
return rational.int_to_Q()
elif ZZ.has_coerce_map_from(S):
return rational.Z_to_Q() * ZZ._internal_coerce_map_from(S)
from sage.rings.localization import Localization
if isinstance(S, Localization):
if S.fraction_field() is self:
from sage.structure.coerce_maps import CallableConvertMap
return CallableConvertMap(S,
self,
lambda x: x._value,
parent_as_first_arg=False)
def _coerce_map_from_(self, other):
r"""
TESTS::
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import *
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_ring import MonoidPowerSeriesRing
sage: mps = MonoidPowerSeriesRing(QQ, NNMonoid(False))
sage: mps.has_coerce_map_from( MonoidPowerSeriesRing(ZZ, NNMonoid(False)) ) # indirect doctest
True
"""
if isinstance(other, MonoidPowerSeriesAmbient_abstract):
if self.monoid() == other.monoid() and \
self.coefficient_domain().has_coerce_map_from(other.coefficient_domain()) :
from sage.structure.coerce_maps import CallableConvertMap
return CallableConvertMap(other, self,
self._element_constructor_)
def _coerce_map_from_(self, R):
"""
EXAMPLES::
sage: L.<x,y> = LaurentPolynomialRing(QQ)
sage: L.coerce_map_from(QQ)
Composite map:
From: Rational Field
To: Multivariate Laurent Polynomial Ring in x, y over Rational Field
Defn: Polynomial base injection morphism:
From: Rational Field
To: Multivariate Polynomial Ring in x, y over Rational Field
then
Call morphism:
From: Multivariate Polynomial Ring in x, y over Rational Field
To: Multivariate Laurent Polynomial Ring in x, y over Rational Field
Let us check that coercion between Laurent Polynomials over
different base rings works (:trac:`15345`)::
sage: R = LaurentPolynomialRing(ZZ, 'x')
sage: T = LaurentPolynomialRing(QQ, 'x')
sage: R.gen() + 3*T.gen()
4*x
"""
if R is self._R or (isinstance(R, LaurentPolynomialRing_generic)
and self._R.has_coerce_map_from(R._R)):
from sage.structure.coerce_maps import CallableConvertMap
return CallableConvertMap(R,
self,
self._element_constructor_,
parent_as_first_arg=False)
elif isinstance(R, LaurentPolynomialRing_generic) and \
R.variable_names() == self.variable_names() and \
self.base_ring().has_coerce_map_from(R.base_ring()):
return True
f = self._R.coerce_map_from(R)
if f is not None:
from sage.categories.homset import Hom
from sage.categories.morphism import CallMorphism
return CallMorphism(Hom(self._R, self)) * f
def _coerce_map_from_(self, other):
"""
TESTS::
sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_ambient import *
sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_testtype import *
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import *
sage: ma = ModularFormsAmbient( QQ, ModularFormTestType_scalar(), NNFilter(5) )
sage: ma._coerce_map_from_(ma)
Conversion via _element_constructor_ map:
From: Graded expansion ring with generators g1, g2, g3, g4, g5
To: Graded expansion ring with generators g1, g2, g3, g4, g5
"""
from sage.structure.coerce_maps import CallableConvertMap
if isinstance(other, ModularFormsRing_generic) and \
self.base_ring().has_coerce_map_from(other.base_ring()) and \
self.type().is_vector_valued() and \
self.type().non_vector_valued() == other.type() :
return CallableConvertMap(other, self, self._element_constructor_)
return ModularFormsAmbient_abstract._coerce_map_from_(self, other)
def _coerce_map_from_(self, other):
r"""
TODO:
This is a stub. The dream is that representations know about
compatible coercions and so would actions and characters. Then
every equivariant monoid power series ring would be a functorial
construction in all three parameters (The functor would then be
applied to a representation within a universe of representations).
TESTS::
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import *
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_ring import EquivariantMonoidPowerSeriesRing
sage: emps = EquivariantMonoidPowerSeriesRing(NNMonoid(True), TrivialCharacterMonoid("1", QQ), TrivialRepresentation("1", QQ))
sage: emps.has_coerce_map_from( EquivariantMonoidPowerSeriesRing(NNMonoid(True), TrivialCharacterMonoid("1", QQ), TrivialRepresentation("1", ZZ)) ) # indirect doctest
True
"""
if isinstance(other, EquivariantMonoidPowerSeriesAmbient_abstract):
if self.action() == other.action() and \
self.characters() == other.characters() :
if self.representation().extends(other.representation()):
from sage.structure.coerce_maps import CallableConvertMap
return CallableConvertMap(other, self,
self._element_constructor_)
def _coerce_map_from_(self, S):
"""
Return ``True`` if elements of ``S`` can be coerced into this
fraction field.
This fraction field has coercions from:
- itself
- any fraction field where the base ring coerces to the base
ring of this fraction field
- any ring that coerces to the base ring of this fraction field
EXAMPLES::
sage: F = QQ['x,y'].fraction_field()
sage: F.has_coerce_map_from(F) # indirect doctest
True
::
sage: F.has_coerce_map_from(ZZ['x,y'].fraction_field())
True
::
sage: F.has_coerce_map_from(ZZ['x,y,z'].fraction_field())
False
::
sage: F.has_coerce_map_from(ZZ)
True
Test coercions::
sage: F.coerce(1)
1
sage: F.coerce(int(1))
1
sage: F.coerce(1/2)
1/2
::
sage: K = ZZ['x,y'].fraction_field()
sage: x,y = K.gens()
sage: F.coerce(F.gen())
x
sage: F.coerce(x)
x
sage: F.coerce(x/y)
x/y
sage: L = ZZ['x'].fraction_field()
sage: K.coerce(L.gen())
x
We demonstrate that :trac:`7958` is resolved in the case of
number fields::
sage: _.<x> = ZZ[]
sage: K.<a> = NumberField(x^5-3*x^4+2424*x^3+2*x-232)
sage: R.<b> = K.ring_of_integers()
sage: S.<y> = R[]
sage: F = FractionField(S)
sage: F(1/a)
(a^4 - 3*a^3 + 2424*a^2 + 2)/232
Some corner cases have been known to fail in the past (:trac:`5917`)::
sage: F1 = FractionField( QQ['a'] )
sage: R12 = F1['x','y']
sage: R12('a')
a
sage: F1(R12(F1('a')))
a
sage: F2 = FractionField( QQ['a','b'] )
sage: R22 = F2['x','y']
sage: R22('a')
a
sage: F2(R22(F2('a')))
a
Coercion from Laurent polynomials now works (:trac:`15345`)::
sage: R = LaurentPolynomialRing(ZZ, 'x')
sage: T = PolynomialRing(ZZ, 'x')
sage: R.gen() + FractionField(T).gen()
2*x
sage: 1/(R.gen() + 1)
1/(x + 1)
sage: R = LaurentPolynomialRing(ZZ, 'x,y')
sage: FF = FractionField(PolynomialRing(ZZ, 'x,y'))
sage: prod(R.gens()) + prod(FF.gens())
2*x*y
sage: 1/(R.gen(0) + R.gen(1))
1/(x + y)
"""
from sage.rings.integer_ring import ZZ
from sage.rings.rational_field import QQ
from sage.rings.number_field.number_field_base import NumberField
from sage.rings.polynomial.laurent_polynomial_ring import \
LaurentPolynomialRing_generic
# The case ``S`` being `\QQ` requires special handling since `\QQ` is
# not implemented as a ``FractionField_generic``.
if S is QQ and self._R.has_coerce_map_from(ZZ):
return CallableConvertMap(S, self, \
lambda x: self._element_class(self, x.numerator(),
x.denominator()), parent_as_first_arg=False)
# Number fields also need to be handled separately.
if isinstance(S, NumberField):
return CallableConvertMap(S, self, \
self._number_field_to_frac_of_ring_of_integers, \
parent_as_first_arg=False)
# special treatment for LaurentPolynomialRings
if isinstance(S, LaurentPolynomialRing_generic):
def converter(x, y=None):
if y is None:
return self._element_class(self, *x._fraction_pair())
xnum, xden = x._fraction_pair()
ynum, yden = y._fraction_pair()
return self._element_class(self, xnum * yden, xden * ynum)
return CallableConvertMap(S,
self,
converter,
parent_as_first_arg=False)
if isinstance(S, FractionField_generic) and \
self._R.has_coerce_map_from(S.ring()):
return CallableConvertMap(S, self, \
lambda x: self._element_class(self, x.numerator(),
x.denominator()), parent_as_first_arg=False)
if self._R.has_coerce_map_from(S):
return CallableConvertMap(S,
self,
self._element_class,
parent_as_first_arg=True)
return None
def _coerce_map_from_(self, S):
"""
Return ``True`` if elements of ``S`` can be coerced into this
fraction field.
This fraction field has coercions from:
- itself
- any fraction field where the base ring coerces to the base
ring of this fraction field
- any ring that coerces to the base ring of this fraction field
EXAMPLES::
sage: F = QQ['x,y'].fraction_field()
sage: F.has_coerce_map_from(F) # indirect doctest
True
::
sage: F.has_coerce_map_from(ZZ['x,y'].fraction_field())
True
::
sage: F.has_coerce_map_from(ZZ['x,y,z'].fraction_field())
False
::
sage: F.has_coerce_map_from(ZZ)
True
Test coercions::
sage: F.coerce(1)
1
sage: F.coerce(int(1))
1
sage: F.coerce(1/2)
1/2
::
sage: K = ZZ['x,y'].fraction_field()
sage: x,y = K.gens()
sage: F.coerce(F.gen())
x
sage: F.coerce(x)
x
sage: F.coerce(x/y)
x/y
sage: L = ZZ['x'].fraction_field()
sage: K.coerce(L.gen())
x
We demonstrate that :trac:`7958` is resolved in the case of
number fields::
sage: _.<x> = ZZ[]
sage: K.<a> = NumberField(x^5-3*x^4+2424*x^3+2*x-232)
sage: R.<b> = K.ring_of_integers()
sage: S.<y> = R[]
sage: F = FractionField(S)
sage: F(1/a)
(a^4 - 3*a^3 + 2424*a^2 + 2)/232
Some corner cases have been known to fail in the past (:trac:`5917`)::
sage: F1 = FractionField( QQ['a'] )
sage: R12 = F1['x','y']
sage: R12('a')
a
sage: F1(R12(F1('a')))
a
sage: F2 = FractionField( QQ['a','b'] )
sage: R22 = F2['x','y']
sage: R22('a')
a
sage: F2(R22(F2('a')))
a
"""
from sage.rings.integer_ring import ZZ
from sage.rings.rational_field import QQ
from sage.rings.number_field.number_field_base import NumberField
# The case ``S`` being `\QQ` requires special handling since `\QQ` is
# not implemented as a ``FractionField_generic``.
if S is QQ and self._R.has_coerce_map_from(ZZ):
return CallableConvertMap(S, self, \
lambda x: self._element_class(self, x.numerator(),
x.denominator()), parent_as_first_arg=False)
# Number fields also need to be handled separately.
if isinstance(S, NumberField):
return CallableConvertMap(S, self, \
self._number_field_to_frac_of_ring_of_integers, \
parent_as_first_arg=False)
if isinstance(S, FractionField_generic) and \
self._R.has_coerce_map_from(S.ring()):
return CallableConvertMap(S, self, \
lambda x: self._element_class(self, x.numerator(),
x.denominator()), parent_as_first_arg=False)
if self._R.has_coerce_map_from(S):
return CallableConvertMap(S,
self,
self._element_class,
parent_as_first_arg=True)
return None