def __init__(self,
A,
stream=None,
order=None,
aorder=None,
aorder_changed=True,
is_initialized=False,
name=None):
"""
EXAMPLES::
sage: L = LazyPowerSeriesRing(QQ)
sage: f = L()
sage: loads(dumps(f))
Uninitialized lazy power series
"""
AlgebraElement.__init__(self, A)
self._stream = stream
self.order = unk if order is None else order
self.aorder = unk if aorder is None else aorder
if self.aorder == inf:
self.order = inf
self.aorder_changed = aorder_changed
self.is_initialized = is_initialized
self._zero = A.base_ring().zero_element()
self._name = name
def __init__(self, parent, x, check):
r""" Create an element of the parent group algebra. Not intended to be
called by the user; see GroupAlgebra.__call__ for examples and
doctests."""
AlgebraElement.__init__(self, parent)
if not hasattr(x, 'parent'):
x = IntegerRing(
)(x) # occasionally coercion framework tries to pass a Python int
if isinstance(x, FormalSum):
if check:
for c, d in x._data:
if d.parent() != self.parent().group():
raise TypeError("%s is not an element of group %s" %
(d, self.parent().group()))
self._fs = x
else:
self._fs = x
elif self.base_ring().has_coerce_map_from(x.parent()):
self._fs = self.parent()._formal_sum_module([
(x, self.parent().group()(1))
])
elif self.parent().group().has_coerce_map_from(x.parent()):
self._fs = self.parent()._formal_sum_module([
(1, self.parent().group()(x))
])
else:
raise TypeError(
"Don't know how to create an element of %s from %s" %
(self.parent(), x))
def __init__(self, A, x):
"""
Create the element x of the FreeAlgebra A.
"""
if isinstance(x, FreeAlgebraElement):
x = x.__monomial_coefficients
AlgebraElement.__init__(self, A)
R = A.base_ring()
if isinstance(x, AlgebraElement): #and x.parent() == A.base_ring():
self.__monomial_coefficients = { A.monoid()(1):R(x) }
elif isinstance(x, FreeMonoidElement):
self.__monomial_coefficients = { x:R(1) }
elif True:
self.__monomial_coefficients = dict([ (A.monoid()(e1),R(e2)) for e1,e2 in x.items()])
else:
raise TypeError("Argument x (= %s) is of the wrong type."%x)
def __init__(self, A, stream=None, order=None, aorder=None, aorder_changed=True, is_initialized=False, name=None):
"""
EXAMPLES::
sage: L = LazyPowerSeriesRing(QQ)
sage: f = L()
sage: loads(dumps(f))
Uninitialized lazy power series
"""
AlgebraElement.__init__(self, A)
self._stream = stream
self.order = unk if order is None else order
self.aorder = unk if aorder is None else aorder
if self.aorder == inf:
self.order = inf
self.aorder_changed = aorder_changed
self.is_initialized = is_initialized
self._zero = A.base_ring().zero_element()
self._name = name
def __init__(self, parent, precision, coefficient_function, components, bounding_precision ) :
r"""
INPUT:
- ``parent`` -- An instance of :class:~`fourier_expansion_framework.monoidpowerseries.monoidpowerseries_ambient.MonoidPowerSeriesAmbient_abstract`.
- ``precision`` -- A filter for the parent's action.
- ``coefficient_function`` -- A function returning for each pair of characters and
monoid element a Fourier coefficients.
- ``components`` -- ``None`` or a list of characters. A list of components that do not
vanish. If ``None`` no component is assumed to be zero.
TESTS::
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_lazyelement import *
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_ring import *
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import *
sage: emps = EquivariantMonoidPowerSeriesRing( NNMonoid(), TrivialCharacterMonoid("1", QQ), TrivialRepresentation("1", QQ) )
sage: h = EquivariantMonoidPowerSeries_algebraelement_lazy(emps, emps.action().filter(3), lambda (ch, k) : 1, None, None)
"""
AlgebraElement.__init__(self, parent)
EquivariantMonoidPowerSeries_abstract_lazy.__init__(self, parent, precision,
coefficient_function, components, bounding_precision)
def __init__(self, parent, polynomial) :
"""
INPUT:
- ``parent`` -- An instance of :class:~`fourier_expansion_framework.gradedexpansions.gradedexpansion_ring.GradedExpansionRing_class`.
- ``polynomial`` -- A polynomial in the polynomial ring underlying the parent.
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: from psage.modform.fourier_expansion_framework.gradedexpansions.gradedexpansion_element import *
sage: mps = MonoidPowerSeriesRing(QQ, NNMonoid(False))
sage: P.<a,b> = QQ[]
sage: ger = GradedExpansionRing_class(Sequence([MonoidPowerSeries(mps, {1: 1}, mps.monoid().filter(4))]), Sequence([MonoidPowerSeries(mps, {1: 1, 2: 3}, mps.monoid().filter(4))]), P.ideal(a - b), DegreeGrading((1,2)))
sage: h = GradedExpansion_class(ger, a^2)
"""
AlgebraElement.__init__(self, parent)
GradedExpansion_abstract.__init__(self, parent, polynomial)
def __init__(self, parent, precision, coefficient_function, components,
bounding_precision):
r"""
INPUT:
- ``parent`` -- An instance of :class:~`fourier_expansion_framework.monoidpowerseries.monoidpowerseries_ambient.MonoidPowerSeriesAmbient_abstract`.
- ``precision`` -- A filter for the parent's action.
- ``coefficient_function`` -- A function returning for each pair of characters and
monoid element a Fourier coefficients.
- ``components`` -- ``None`` or a list of characters. A list of components that do not
vanish. If ``None`` no component is assumed to be zero.
TESTS::
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_lazyelement import *
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_ring import *
sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import *
sage: emps = EquivariantMonoidPowerSeriesRing( NNMonoid(), TrivialCharacterMonoid("1", QQ), TrivialRepresentation("1", QQ) )
sage: h = EquivariantMonoidPowerSeries_algebraelement_lazy(emps, emps.action().filter(3), lambda (ch, k) : 1, None, None)
"""
AlgebraElement.__init__(self, parent)
EquivariantMonoidPowerSeries_abstract_lazy.__init__(
self, parent, precision, coefficient_function, components,
bounding_precision)
def __init__(self, A, x):
"""
Create the element ``x`` of the FreeAlgebra ``A``.
TESTS::
sage: F.<x,y,z> = FreeAlgebra(QQ, 3)
sage: elt = x^3 * y - z^2*x
sage: TestSuite(elt).run()
"""
if isinstance(x, FreeAlgebraElement):
x = x.__monomial_coefficients
AlgebraElement.__init__(self, A)
R = A.base_ring()
if isinstance(x, AlgebraElement): #and x.parent() == A.base_ring():
self.__monomial_coefficients = { A.monoid()(1):R(x) }
elif isinstance(x, FreeMonoidElement):
self.__monomial_coefficients = { x:R(1) }
elif True:
self.__monomial_coefficients = dict([ (A.monoid()(e1),R(e2)) for e1,e2 in x.items()])
else:
raise TypeError("Argument x (= %s) is of the wrong type."%x)
def __init__(self, A, x):
"""
Create the element ``x`` of the FreeAlgebra ``A``.
TESTS::
sage: F.<x,y,z> = FreeAlgebra(QQ, 3)
sage: elt = x^3 * y - z^2*x
sage: TestSuite(elt).run()
"""
if isinstance(x, FreeAlgebraElement):
x = x.__monomial_coefficients
AlgebraElement.__init__(self, A)
R = A.base_ring()
if isinstance(x, AlgebraElement): #and x.parent() == A.base_ring():
self.__monomial_coefficients = {A.monoid()(1): R(x)}
elif isinstance(x, FreeMonoidElement):
self.__monomial_coefficients = {x: R(1)}
elif True:
self.__monomial_coefficients = dict([(A.monoid()(e1), R(e2))
for e1, e2 in x.items()])
else:
raise TypeError("Argument x (= %s) is of the wrong type." % x)
def __init__(self, parent, x, check):
r""" Create an element of the parent group algebra. Not intended to be
called by the user; see GroupAlgebra.__call__ for examples and
doctests."""
AlgebraElement.__init__(self, parent)
if not hasattr(x, 'parent'):
x = IntegerRing()(x) # occasionally coercion framework tries to pass a Python int
if isinstance(x, FormalSum):
if check:
for c,d in x._data:
if d.parent() != self.parent().group():
raise TypeError("%s is not an element of group %s" % (d, self.parent().group()))
self._fs = x
else:
self._fs = x
elif self.base_ring().has_coerce_map_from(x.parent()):
self._fs = self.parent()._formal_sum_module([ (x, self.parent().group()(1)) ])
elif self.parent().group().has_coerce_map_from(x.parent()):
self._fs = self.parent()._formal_sum_module([ (1, self.parent().group()(x)) ])
else:
raise TypeError("Don't know how to create an element of %s from %s" % (self.parent(), x))
def __init__(self, A, x):
"""
Create the element x of the FreeAlgebraQuotient A.
EXAMPLES::
sage: H, (i,j,k) = sage.algebras.free_algebra_quotient.hamilton_quatalg(ZZ)
sage: sage.algebras.free_algebra_quotient.FreeAlgebraQuotientElement(H, i)
i
sage: a = sage.algebras.free_algebra_quotient.FreeAlgebraQuotientElement(H, 1); a
1
sage: a in H
True
TESTS::
sage: TestSuite(i).run()
"""
AlgebraElement.__init__(self, A)
Q = self.parent()
if isinstance(x, FreeAlgebraQuotientElement) and x.parent() == Q:
self.__vector = Q.module()(x.vector())
return
if isinstance(x, (int, long, Integer)):
self.__vector = Q.module().gen(0) * x
return
elif isinstance(x, FreeModuleElement) and x.parent() is Q.module():
self.__vector = x
return
elif isinstance(x, FreeModuleElement) and x.parent() == A.module():
self.__vector = x
return
R = A.base_ring()
M = A.module()
F = A.monoid()
B = A.monomial_basis()
if isinstance(x, (int, long, Integer)):
self.__vector = x*M.gen(0)
elif isinstance(x, RingElement) and not isinstance(x, AlgebraElement) and x in R:
self.__vector = x * M.gen(0)
elif isinstance(x, FreeMonoidElement) and x.parent() is F:
if x in B:
self.__vector = M.gen(B.index(x))
else:
raise AttributeError("Argument x (= %s) is not in monomial basis"%x)
elif isinstance(x, list) and len(x) == A.dimension():
try:
self.__vector = M(x)
except TypeError:
raise TypeError("Argument x (= %s) is of the wrong type."%x)
elif isinstance(x, FreeAlgebraElement) and x.parent() is A.free_algebra():
# Need to do more work here to include monomials not
# represented in the monomial basis.
self.__vector = M(0)
for m, c in x._FreeAlgebraElement__monomial_coefficients.iteritems():
self.__vector += c*M.gen(B.index(m))
elif isinstance(x, dict):
self.__vector = M(0)
for m, c in x.iteritems():
self.__vector += c*M.gen(B.index(m))
elif isinstance(x, AlgebraElement) and x.parent().ambient_algebra() is A:
self.__vector = x.ambient_algebra_element().vector()
else:
raise TypeError("Argument x (= %s) is of the wrong type."%x)
def __init__(self, A, x):
"""
Create the element x of the FreeAlgebraQuotient A.
EXAMPLES::
sage: H, (i,j,k) = sage.algebras.free_algebra_quotient.hamilton_quatalg(ZZ)
sage: sage.algebras.free_algebra_quotient.FreeAlgebraQuotientElement(H, i)
i
sage: a = sage.algebras.free_algebra_quotient.FreeAlgebraQuotientElement(H, 1); a
1
sage: a in H
True
TESTS::
sage: TestSuite(i).run()
"""
AlgebraElement.__init__(self, A)
Q = self.parent()
if isinstance(x, FreeAlgebraQuotientElement) and x.parent() == Q:
self.__vector = Q.module()(x.vector())
return
if isinstance(x, (int, long, Integer)):
self.__vector = Q.module().gen(0) * x
return
elif isinstance(x, FreeModuleElement) and x.parent() is Q.module():
self.__vector = x
return
elif isinstance(x, FreeModuleElement) and x.parent() == A.module():
self.__vector = x
return
R = A.base_ring()
M = A.module()
F = A.monoid()
B = A.monomial_basis()
if isinstance(x, (int, long, Integer)):
self.__vector = x * M.gen(0)
elif isinstance(
x,
RingElement) and not isinstance(x, AlgebraElement) and x in R:
self.__vector = x * M.gen(0)
elif isinstance(x, FreeMonoidElement) and x.parent() is F:
if x in B:
self.__vector = M.gen(B.index(x))
else:
raise AttributeError, \
"Argument x (= %s) is not in monomial basis"%x
elif isinstance(x, list) and len(x) == A.dimension():
try:
self.__vector = M(x)
except TypeError:
raise TypeError, "Argument x (= %s) is of the wrong type." % x
elif isinstance(x,
FreeAlgebraElement) and x.parent() is A.free_algebra():
# Need to do more work here to include monomials not
# represented in the monomial basis.
self.__vector = M(0)
for m, c in x._FreeAlgebraElement__monomial_coefficients.iteritems(
):
self.__vector += c * M.gen(B.index(m))
elif isinstance(x, dict):
self.__vector = M(0)
for m, c in x.iteritems():
self.__vector += c * M.gen(B.index(m))
elif isinstance(x,
AlgebraElement) and x.parent().ambient_algebra() is A:
self.__vector = x.ambient_algebra_element().vector()
else:
raise TypeError, "Argument x (= %s) is of the wrong type." % x