def __init__(self, A, S) :
r"""
INPUT:
- `A` -- A ring.
- `S` -- A monoid as implemented in :class:~`fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids.NNMonoid`.
TESTS::
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import *
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_ring import MonoidPowerSeriesRing_generic
sage: mps = MonoidPowerSeriesRing_generic(QQ, NNMonoid(False))
sage: mps = MonoidPowerSeriesRing_generic(ZZ, NNMonoid(False))
sage: mps.base_ring()
Integer Ring
sage: (1 / 2) * mps.0
Monoid power series in Ring of monoid power series over NN
"""
Algebra.__init__(self, A)
MonoidPowerSeriesAmbient_abstract.__init__(self, A, S)
self.__monoid_gens = \
[ self._element_class(self, dict([(s, A.one_element())]),
self.monoid().filter_all() )
for s in S.gens() ]
from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_functor import MonoidPowerSeriesBaseRingInjection
self._populate_coercion_lists_(
coerce_list = [MonoidPowerSeriesBaseRingInjection(self.base_ring(), self)] + \
([S] if isinstance(S, Parent) else []) )
def _element_constructor_(self, x) :
"""
TESTS::
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import *
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_ring import MonoidPowerSeriesRing_generic
sage: mps = MonoidPowerSeriesRing_generic(QQ, NNMonoid(False))
sage: h = mps(1) # indirect doctest
sage: h = mps(mps.monoid().zero_element())
sage: h = mps.zero_element()
sage: K.<rho> = CyclotomicField(6)
sage: mps = MonoidPowerSeriesRing_generic(K, NNMonoid(False))
sage: h = mps(rho)
sage: h = mps(1)
"""
if isinstance(x, int) :
x = Integer(x)
if isinstance(x, Element) :
P = x.parent()
if P is self.coefficient_domain() :
return self._element_class( self, {self.monoid().zero_element(): x},
self.monoid().filter_all() )
elif self.coefficient_domain().has_coerce_map_from(P) :
return self._element_class( self, {self.monoid().zero_element(): self.coefficient_domain()(x)},
self.monoid().filter_all() )
elif P is self.monoid() :
return self._element_class( self, {x: self.base_ring().one_element},
self.monoid().filter_all() )
return MonoidPowerSeriesAmbient_abstract._element_constructor_(self, x)
def _element_constructor_(self, x) :
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_generic
sage: mps = MonoidPowerSeriesRing_generic(QQ, NNMonoid(False))
sage: h = mps(1) # indirect doctest
sage: h = mps(mps.monoid().zero_element())
sage: h = mps.zero_element()
sage: K.<rho> = CyclotomicField(6)
sage: mps = MonoidPowerSeriesRing_generic(K, NNMonoid(False))
sage: h = mps(rho)
sage: h = mps(1)
"""
if isinstance(x, int) :
x = Integer(x)
if isinstance(x, Element) :
P = x.parent()
if P is self.coefficient_domain() :
return self._element_class( self, {self.monoid().zero_element(): x},
self.monoid().filter_all() )
elif self.coefficient_domain().has_coerce_map_from(P) :
return self._element_class( self, {self.monoid().zero_element(): self.coefficient_domain()(x)},
self.monoid().filter_all() )
elif P is self.monoid() :
return self._element_class( self, {x: self.base_ring().one_element},
self.monoid().filter_all() )
return MonoidPowerSeriesAmbient_abstract._element_constructor_(self, x)
def __init__(self, A, S) :
"""
INPUT:
- `A` -- A module.
- `S` -- A monoid as implemented in :class:~`fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids.NNMonoid`.
TESTS::
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import *
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_module import MonoidPowerSeriesModule_generic
sage: mps = MonoidPowerSeriesModule_generic(FreeModule(QQ,2), NNMonoid(False))
"""
Module.__init__(self, MonoidPowerSeriesRing(A.base_ring(), S))
MonoidPowerSeriesAmbient_abstract.__init__(self, A, S)
self.__coeff_gens = \
[ self._element_class(self, dict([(S.zero_element(), a)]),
self.monoid().filter_all() )
for a in A.gens() ]
def __init__(self, A, S) :
r"""
INPUT:
- `A` -- A module.
- `S` -- A monoid as implemented in :class:~`fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids.NNMonoid`.
TESTS::
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import *
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_module import MonoidPowerSeriesModule_generic
sage: mps = MonoidPowerSeriesModule_generic(FreeModule(QQ,2), NNMonoid(False))
sage: mps = MonoidPowerSeriesModule_generic(FreeModule(ZZ,2), NNMonoid(False))
sage: mps.base_ring()
Ring of monoid power series over NN
sage: (1 / 2) * mps.0
Monoid power series in Module of monoid power series over NN
"""
Module.__init__(self, MonoidPowerSeriesRing(A.base_ring(), S))
MonoidPowerSeriesAmbient_abstract.__init__(self, A, S)
self.__coeff_gens = \
[ self._element_class(self, dict([(S.zero_element(), a)]),
self.monoid().filter_all() )
for a in A.gens() ]
def _element_constructor_(self, x) :
"""
TESTS::
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import *
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_module import MonoidPowerSeriesModule_generic
sage: mps = MonoidPowerSeriesModule_generic(FreeModule(QQ,2), NNMonoid(False))
sage: h = mps(0) # indirect doctest
sage: h = mps(int(0)) # indirect doctest
"""
if isinstance(x, int) and x == 0 :
return self._element_class( self, dict(),
self.monoid().filter_all() )
if isinstance(x, Element) and x.is_zero() :
P = x.parent()
if self.base_ring().base_ring().has_coerce_map_from(P) :
return self._element_class( self, dict(),
self.monoid().filter_all() )
return MonoidPowerSeriesAmbient_abstract._element_constructor_(self, x)
def _element_constructor_(self, x) :
r"""
TESTS::
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import *
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_module import MonoidPowerSeriesModule_generic
sage: mps = MonoidPowerSeriesModule_generic(FreeModule(QQ,2), NNMonoid(False))
sage: h = mps(0) # indirect doctest
sage: h = mps(int(0)) # indirect doctest
"""
if isinstance(x, int) and x == 0 :
return self._element_class( self, dict(),
self.monoid().filter_all() )
if isinstance(x, Element) and x.is_zero() :
P = x.parent()
if self.base_ring().base_ring().has_coerce_map_from(P) :
return self._element_class( self, dict(),
self.monoid().filter_all() )
return MonoidPowerSeriesAmbient_abstract._element_constructor_(self, x)
