def __init__(self, analytic_type, group, red_hom):
r"""
Construction functor for the forms ring
with the given ``analytic_type``, ``group``
and variable ``red_hom``
See :meth:`__call__` for a description of the functor.
INPUT:
- ``analytic_type`` -- An element of ``AnalyticType()``.
- ``group`` -- The index of a Hecke Triangle group.
- ``red_hom`` -- A boolean variable for the parameter ``red_hom``
(also see ``FormsRing_abstract``).
OUTPUT:
The construction functor for the corresponding forms ring.
EXAMPLES::
sage: from sage.modular.modform_hecketriangle.functors import FormsRingFunctor
sage: FormsRingFunctor(["quasi", "mero"], group=6, red_hom=False)
QuasiMeromorphicModularFormsRingFunctor(n=6)
sage: FormsRingFunctor(["quasi", "mero"], group=6, red_hom=True)
QuasiMeromorphicModularFormsRingFunctor(n=6, red_hom=True)
"""
Functor.__init__(self, Rings(), Rings())
from .graded_ring import canonical_parameters
(self._group, R, red_hom, n) = canonical_parameters(group, ZZ, red_hom)
self._red_hom = bool(red_hom)
self._analytic_type = self.AT(analytic_type)
def __init__(self, analytic_type, group, red_hom):
r"""
Construction functor for the forms ring
with the given ``analytic_type``, ``group``
and variable ``red_hom``
See :meth:`__call__` for a description of the functor.
INPUT:
- ``analytic_type`` -- An element of ``AnalyticType()``.
- ``group`` -- The index of a Hecke Triangle group.
- ``red_hom`` -- A boolean variable for the parameter ``red_hom``
(also see ``FormsRing_abstract``).
OUTPUT:
The construction functor for the corresponding forms ring.
EXAMPLES::
sage: from sage.modular.modform_hecketriangle.functors import FormsRingFunctor
sage: FormsRingFunctor(["quasi", "mero"], group=6, red_hom=False)
QuasiMeromorphicModularFormsRingFunctor(n=6)
sage: FormsRingFunctor(["quasi", "mero"], group=6, red_hom=True)
QuasiMeromorphicModularFormsRingFunctor(n=6, red_hom=True)
"""
Functor.__init__(self, Rings(), Rings())
from .graded_ring import canonical_parameters
(self._group, R, red_hom, n) = canonical_parameters(group, ZZ, red_hom)
self._red_hom = bool(red_hom)
self._analytic_type = self.AT(analytic_type)
def __init__(self, analytic_type, group, k, ep):
r"""
Construction functor for the forms space
(or forms ring, see above) with
the given ``analytic_type``, ``group``,
weight ``k`` and multiplier ``ep``.
See :meth:`__call__` for a description of the functor.
INPUT:
- ``analytic_type`` -- An element of ``AnalyticType()``.
- ``group`` -- The index of a Hecke Triangle group.
- ``k`` -- A rational number, the weight of the space.
- ``ep`` -- `1` or `-1`, the multiplier of the space.
OUTPUT:
The construction functor for the corresponding forms space/ring.
EXAMPLES::
sage: from sage.modular.modform_hecketriangle.functors import FormsSpaceFunctor
sage: FormsSpaceFunctor(["holo", "weak"], group=4, k=0, ep=-1)
WeakModularFormsFunctor(n=4, k=0, ep=-1)
"""
Functor.__init__(self, Rings(), CommutativeAdditiveGroups())
from .space import canonical_parameters
(self._group, R, self._k, self._ep, n) = canonical_parameters(group, ZZ, k, ep)
self._analytic_type = self.AT(analytic_type)
def __init__(self, analytic_type, group, k, ep):
r"""
Construction functor for the forms space
(or forms ring, see above) with
the given ``analytic_type``, ``group``,
weight ``k`` and multiplier ``ep``.
See :meth:`__call__` for a description of the functor.
INPUT:
- ``analytic_type`` -- An element of ``AnalyticType()``.
- ``group`` -- The index of a Hecke Triangle group.
- ``k`` -- A rational number, the weight of the space.
- ``ep`` -- `1` or `-1`, the multiplier of the space.
OUTPUT:
The construction functor for the corresponding forms space/ring.
EXAMPLES::
sage: from sage.modular.modform_hecketriangle.functors import FormsSpaceFunctor
sage: FormsSpaceFunctor(["holo", "weak"], group=4, k=0, ep=-1)
WeakModularFormsFunctor(n=4, k=0, ep=-1)
"""
Functor.__init__(self, Rings(), CommutativeAdditiveGroups())
from .space import canonical_parameters
(self._group, R, self._k, self._ep, n) = canonical_parameters(group, ZZ, k, ep)
self._analytic_type = self.AT(analytic_type)
def __init__(self, vars):
"""
EXAMPLES::
sage: F = sage.combinat.free_prelie_algebra.PreLieFunctor(['x','y'])
sage: F
PreLie[x,y]
sage: F(ZZ)
Free PreLie algebra on 2 generators ['x', 'y'] over Integer Ring
"""
Functor.__init__(self, Rings(), Magmas())
self.vars = vars
def __init__(self, vars):
"""
EXAMPLES::
sage: F = sage.algebras.free_zinbiel_algebra.ZinbielFunctor(['x','y'])
sage: F
Zinbiel[x,y]
sage: F(ZZ)
Free Zinbiel algebra on generators (Z[x], Z[y]) over Integer Ring
"""
Functor.__init__(self, Rings(), Magmas())
self.vars = vars
def __init__(self, vars):
"""
EXAMPLES::
sage: F = sage.combinat.free_dendriform_algebra.DendriformFunctor(['x','y'])
sage: F
Dendriform[x,y]
sage: F(ZZ)
Free Dendriform algebra on 2 generators ['x', 'y'] over Integer Ring
"""
Functor.__init__(self, Rings(), Rings())
self.vars = vars
def __init__(self, vars):
"""
EXAMPLES::
sage: F = sage.combinat.free_prelie_algebra.PreLieFunctor(['x','y'])
sage: F
PreLie[x,y]
sage: F(ZZ)
Free PreLie algebra on 2 generators ['x', 'y'] over Integer Ring
"""
Functor.__init__(self, Rings(), Magmas())
self.vars = vars
def __init__(self, vars):
"""
EXAMPLES::
sage: F = sage.combinat.free_dendriform_algebra.DendriformFunctor(['x','y'])
sage: F
Dendriform[x,y]
sage: F(ZZ)
Free Dendriform algebra on 2 generators ['x', 'y'] over Integer Ring
"""
Functor.__init__(self, Rings(), Rings())
self.vars = vars
def __init__(self, vars):
"""
EXAMPLES::
sage: F = sage.algebras.free_zinbiel_algebra.ZinbielFunctor(['x','y'])
sage: F
Zinbiel[x,y]
sage: F(ZZ)
Free Zinbiel algebra on generators (Z[x], Z[y]) over Integer Ring
"""
Functor.__init__(self, Rings(), Magmas())
self.vars = vars
def __init__(self):
r"""
Initialize the :class:`GroupExp` functor.
EXAMPLES::
sage: F = GroupExp()
sage: F.domain()
Category of commutative additive groups
sage: F.codomain()
Category of groups
"""
Functor.__init__(self, CommutativeAdditiveGroups(), Groups())
def __init__(self):
r"""
Initialize the :class:`GroupExp` functor.
EXAMPLES::
sage: F = GroupExp()
sage: F.domain()
Category of commutative additive groups
sage: F.codomain()
Category of groups
"""
Functor.__init__(self, CommutativeAdditiveGroups(), Groups())
def __init__(self, variables):
"""
EXAMPLES::
sage: functor = sage.algebras.free_zinbiel_algebra.ZinbielFunctor
sage: F = functor(['x','y']); F
Zinbiel[x,y]
sage: F(ZZ)
Free Zinbiel algebra on generators (Z[x], Z[y]) over Integer Ring
"""
Functor.__init__(self, Rings(), Magmas())
self.vars = variables
self._finite_vars = bool(
isinstance(variables, (list, tuple))
or variables in Sets().Finite())
def __init__(self, ambient_space_functor, generators):
r"""
Construction functor for the forms sub space
for the given ``generators`` inside the ambient space
which is constructed by the ``ambient_space_functor``.
The functor can only be applied to rings for which the generators
can be converted into the corresponding forms space
given by the ``ambient_space_functor`` applied to the ring.
See :meth:`__call__` for a description of the functor.
INPUT:
- ``ambient_space_functor`` -- A FormsSpaceFunctor
- ``generators`` -- A list of elements of some ambient space
over some base ring.
OUTPUT:
The construction functor for the corresponding forms sub space.
EXAMPLES::
sage: from sage.modular.modform_hecketriangle.functors import (FormsSpaceFunctor, FormsSubSpaceFunctor)
sage: from sage.modular.modform_hecketriangle.space import ModularForms
sage: ambient_space = ModularForms(n=4, k=12, ep=1)
sage: ambient_space_functor = FormsSpaceFunctor("holo", group=4, k=12, ep=1)
sage: ambient_space_functor
ModularFormsFunctor(n=4, k=12, ep=1)
sage: el = ambient_space.gen(0).full_reduce()
sage: FormsSubSpaceFunctor(ambient_space_functor, [el])
FormsSubSpaceFunctor with 1 generator for the ModularFormsFunctor(n=4, k=12, ep=1)
"""
Functor.__init__(self, Rings(), CommutativeAdditiveGroups())
if not isinstance(ambient_space_functor, FormsSpaceFunctor):
raise ValueError(
"{} is not a FormsSpaceFunctor!".format(ambient_space_functor))
# TODO: canonical parameters? Some checks?
# The generators should have an associated base ring
# self._generators_ring = ...
# on call check if there is a coercion from self._generators_ring to R
self._ambient_space_functor = ambient_space_functor
self._generators = generators
def __init__(self, ambient_space_functor, generators):
r"""
Construction functor for the forms sub space
for the given ``generators`` inside the ambient space
which is constructed by the ``ambient_space_functor``.
The functor can only be applied to rings for which the generators
can be converted into the corresponding forms space
given by the ``ambient_space_functor`` applied to the ring.
See :meth:`__call__` for a description of the functor.
INPUT:
- ``ambient_space_functor`` -- A FormsSpaceFunctor
- ``generators`` -- A list of elements of some ambient space
over some base ring.
OUTPUT:
The construction functor for the corresponding forms sub space.
EXAMPLES::
sage: from sage.modular.modform_hecketriangle.functors import (FormsSpaceFunctor, FormsSubSpaceFunctor)
sage: from sage.modular.modform_hecketriangle.space import ModularForms
sage: ambient_space = ModularForms(n=4, k=12, ep=1)
sage: ambient_space_functor = FormsSpaceFunctor("holo", group=4, k=12, ep=1)
sage: ambient_space_functor
ModularFormsFunctor(n=4, k=12, ep=1)
sage: el = ambient_space.gen(0).full_reduce()
sage: FormsSubSpaceFunctor(ambient_space_functor, [el])
FormsSubSpaceFunctor with 1 generator for the ModularFormsFunctor(n=4, k=12, ep=1)
"""
Functor.__init__(self, Rings(), CommutativeAdditiveGroups())
if not isinstance(ambient_space_functor, FormsSpaceFunctor):
raise ValueError("{} is not a FormsSpaceFunctor!".format(ambient_space_functor))
# TODO: canonical parameters? Some checks?
# The generators should have an associated base ring
# self._generators_ring = ...
# on call check if there is a coercion from self._generators_ring to R
self._ambient_space_functor = ambient_space_functor
self._generators = generators
def __init__(self, x):
Functor.__init__(self, Rings(), Rings())
self.x = x