def _element_constructor_(self, x) :
"""
INPUT:
- `x` -- An integer, an element of the underlying polynomial ring or
an element in a submodule of graded expansions.
OUTPUT:
An instance of the element class.
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_ring import *
sage: mps = MonoidPowerSeriesRing(QQ, NNMonoid(False))
sage: ger = GradedExpansionRing_class(Sequence([MonoidPowerSeries(mps, {1: 1}, mps.monoid().filter(4))]), Sequence([MonoidPowerSeries(mps, {1: 1, 2: 3}, mps.monoid().filter(4))]), PolynomialRing(QQ, ['a', 'b']).ideal(0), DegreeGrading((1,2)))
sage: h = ger(1)
"""
if isinstance(x, (int, Integer)) :
return self._element_class(self, self.relations().ring()(x))
P = x.parent()
if P is self.relations().ring() :
return self._element_class(self, x)
elif self.relations().ring().has_coerce_map_from(P) :
return self._element_class(self, self.relations().ring()(x))
elif P is self.base_ring() and isinstance( self.base_ring(), GradedExpansionAmbient_abstract ) :
return self._element_class(self, self.relations().ring()(x.polynomial()))
return GradedExpansionAmbient_abstract._element_constructor_(self, x)
def _element_constructor_(self, x) :
r"""
INPUT:
- `x` -- A zero integer, an element of the underlying polynomial ring or
an element in a submodule of graded expansions.
OUTPUT:
An instance of the element class.
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: h = ger(0)
"""
if isinstance(x, (int, Integer)) and x == 0 :
return self._element_class(self, self.relations().ring().zero())
P = x.parent()
if P is self.base_ring() :
if x == 0 :
return self._element_class(self, self.relations().ring().zero())
return GradedExpansionAmbient_abstract._element_constructor_(self, x)
def _element_constructor_(self, x):
r"""
INPUT:
- `x` -- A zero integer, an element of the underlying polynomial ring or
an element in a submodule of graded expansions.
OUTPUT:
An instance of the element class.
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: h = ger(0)
"""
if isinstance(x, (int, Integer)) and x == 0:
return self._element_class(self, self.relations().ring().zero())
P = x.parent()
if P is self.base_ring():
if x == 0:
return self._element_class(self,
self.relations().ring().zero())
return GradedExpansionAmbient_abstract._element_constructor_(self, x)
def _element_constructor_(self, x) :
r"""
INPUT:
- `x` -- An integer, an element of the underlying polynomial ring or
an element in a submodule of graded expansions.
OUTPUT:
An instance of the element class.
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_ring import *
sage: mps = MonoidPowerSeriesRing(QQ, NNMonoid(False))
sage: ger = GradedExpansionRing_class(Sequence([MonoidPowerSeries(mps, {1: 1}, mps.monoid().filter(4))]), Sequence([MonoidPowerSeries(mps, {1: 1, 2: 3}, mps.monoid().filter(4))]), PolynomialRing(QQ, ['a', 'b']).ideal(0), DegreeGrading((1,2)))
sage: h = ger(1)
"""
if isinstance(x, (int, Integer)) :
return self._element_class(self, self.relations().ring()(x))
P = x.parent()
if P is self.relations().ring() :
return self._element_class(self, x)
elif self.relations().ring().has_coerce_map_from(P) :
return self._element_class(self, self.relations().ring()(x))
elif P is self.base_ring() and isinstance( self.base_ring(), GradedExpansionAmbient_abstract ) :
return self._element_class(self, self.relations().ring()(x.polynomial()))
return GradedExpansionAmbient_abstract._element_constructor_(self, x)
def __init__ ( self, base_ring_generators, generators,
relations, grading, all_relations = True, reduce_before_evaluating = True) :
"""
The degree one part of the monomials that correspond to generators over the
base expansion ring will serve as the coordinates of the elements.
INPUT:
- ``base_ring_generators`` -- A list of (equivariant) monoid power series with
coefficient domain the base ring of the coefficient
domain of the generators or ``None``.
- ``generators`` -- A list of (equivariant) monoid power series; The generators
of the ambient over the ring generated by the base ring
generators.
- ``relations`` -- An ideal in a polynomial ring with ``len(base_ring_generators) + len(generators)``
variables.
- ``grading`` -- A grading deriving from :class:~`fourier_expansion_framework.gradedexpansions.gradedexpansion_grading`;
A grading for the polynomial ring of the relations.
- ``all_relations`` -- A boolean (default: ``True``); If ``True`` the relations given
for the polynomial ring are all relations that the Fourier
expansion have.
- ``reduce_before_evaluating`` -- A boolean (default: ``True``); If ``True`` any monomial
will be Groebner reduced before the Fourier expansion
is calculated.
NOTE:
The grading must respect the relations of the generators.
TESTS::
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import *
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_ring 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_ring import *
sage: mps = MonoidPowerSeriesRing(QQ, NNMonoid(False))
sage: ger = GradedExpansionRing_class(Sequence([MonoidPowerSeries(mps, {1: 1}, mps.monoid().filter(4))]), Sequence([MonoidPowerSeries(mps, {1: 1, 2: 3}, mps.monoid().filter(4))]), PolynomialRing(QQ, ['a', 'b']).ideal(0), DegreeGrading((1,2)))
sage: ger.base_ring()
Graded expansion ring with generators a
"""
if not hasattr(self, '_element_class') :
self._element_class = GradedExpansion_class
if hasattr(self, "_extended_base_ring") :
Algebra.__init__(self, self._extended_base_ring)
elif base_ring_generators is None or len(base_ring_generators) == 0 :
Algebra.__init__(self, relations.base_ring())
else :
gb = filter( lambda p: all( all(a == 0 for a in list(e)[len(base_ring_generators):])
for e in p.exponents() ),
relations.groebner_basis() )
P = PolynomialRing( relations.base_ring(),
list(relations.ring().variable_names())[:len(base_ring_generators)] )
base_relations = P.ideal(gb)
R = GradedExpansionRing_class(None, base_ring_generators, base_relations,
grading.subgrading(xrange(len(base_ring_generators))), all_relations, reduce_before_evaluating)
Algebra.__init__(self, R)
GradedExpansionAmbient_abstract.__init__(self, base_ring_generators, generators, relations, grading, all_relations, reduce_before_evaluating)
self._populate_coercion_lists_(
coerce_list = [GradedExpansionBaseringInjection(self.base_ring(), self)],
convert_list = [self.relations().ring()],
convert_method_name = "_graded_expansion_submodule_to_graded_ambient_" )
def __init__(self,
base_ring_generators,
generators,
relations,
grading,
all_relations=True,
reduce_before_evaluating=True):
r"""
The degree one part of the monomials that correspond to generators over the
base expansion ring will serve as the coordinates of the elements.
INPUT:
- ``base_ring_generators`` -- A list of (equivariant) monoid power series with
coefficient domain the base ring of the coefficient
domain of the generators or ``None``.
- ``generators`` -- A list of (equivariant) monoid power series; The generators
of the ambient over the ring generated by the base ring
generators.
- ``relations`` -- An ideal in a polynomial ring with ``len(base_ring_generators) + len(generators)``
variables.
- ``grading`` -- A grading deriving from :class:~`fourier_expansion_framework.gradedexpansions.gradedexpansion_grading`;
A grading for the polynomial ring of the relations.
- ``all_relations`` -- A boolean (default: ``True``); If ``True`` the relations given
for the polynomial ring are all relations that the Fourier
expansion have.
- ``reduce_before_evaluating`` -- A boolean (default: ``True``); If ``True`` any monomial
will be Groebner reduced before the Fourier expansion
is calculated.
NOTE:
The grading must respect the relations of the generators.
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.base_ring()
Graded expansion ring with generators a
"""
if not hasattr(self, '_element_class'):
self._element_class = GradedExpansionVector_class
if hasattr(self, "_extended_base_ring"):
Module.__init__(self, self._extended_base_ring)
elif base_ring_generators is None or len(base_ring_generators) == 0:
Module.__init__(self, relations.base_ring())
else:
gb = filter(
lambda p: all(
all(a == 0 for a in list(e)[len(base_ring_generators):])
for e in p.exponents()), relations.groebner_basis())
P = PolynomialRing(
relations.base_ring(),
list(relations.ring().variable_names())
[:len(base_ring_generators)])
base_relations = P.ideal(gb)
R = GradedExpansionRing_class(
None, base_ring_generators, base_relations,
grading.subgrading(xrange(len(base_ring_generators))),
all_relations, reduce_before_evaluating)
Module.__init__(self, R)
GradedExpansionAmbient_abstract.__init__(self, base_ring_generators,
generators, relations,
grading, all_relations,
reduce_before_evaluating)
self._populate_coercion_lists_(
convert_list=[self.relations().ring()],
convert_method_name="_graded_expansion_submodule_to_graded_ambient_"
)
