Functor construction for all spaces¶
AUTHORS:
 Jonas Jermann (2013): initial version

class
sage.modular.modform_hecketriangle.functors.
BaseFacade
(ring)¶ Bases:
sage.structure.parent.Parent
,sage.structure.unique_representation.UniqueRepresentation
BaseFacade of a ring.
This class is used to distinguish the construction of constant elements (modular forms of weight 0) over the given ring and the construction of
FormsRing
orFormsSpace
based on the BaseFacade of the given ring.If that distinction was not made then ring elements couldn’t be considered as constant modular forms in e.g. binary operations. Instead the coercion model would assume that the ring element lies in the common parent of the ring element and e.g. a
FormsSpace
which would give theFormsSpace
over the ring. However this is not correct, theFormsSpace
might (and probably will) not even contain the (constant) ring element. Hence we use theBaseFacade
to distinguish the two cases.Since the
BaseFacade
of a ring embedds into that ring, a common base (resp. a coercion) between the two (or even a more general ring) can be found, namely the ring (not theBaseFacade
of it).

sage.modular.modform_hecketriangle.functors.
ConstantFormsSpaceFunctor
(group)¶ Construction functor for the space of constant forms.
When determining a common parent between a ring and a forms ring or space this functor is first applied to the ring.
EXAMPLES:
sage: from sage.modular.modform_hecketriangle.functors import (ConstantFormsSpaceFunctor, FormsSpaceFunctor) sage: ConstantFormsSpaceFunctor(4) == FormsSpaceFunctor("holo", 4, 0, 1) True sage: ConstantFormsSpaceFunctor(4) ModularFormsFunctor(n=4, k=0, ep=1)

class
sage.modular.modform_hecketriangle.functors.
FormsRingFunctor
(analytic_type, group, red_hom)¶ Bases:
sage.categories.pushout.ConstructionFunctor
Construction functor for forms rings.
NOTE:
When the base ring is not a
BaseFacade
the functor is first merged with the ConstantFormsSpaceFunctor. This case occurs in the pushout constructions. (when trying to find a common parent between a forms ring and a ring which is not aBaseFacade
).
AT
= Analytic Type¶

AnalyticType
¶ alias of
sage.modular.modform_hecketriangle.analytic_type.AnalyticType

merge
(other)¶ Return the merged functor of
self
andother
.It is only possible to merge instances of
FormsSpaceFunctor
andFormsRingFunctor
. Also only if they share the same group. AnFormsSubSpaceFunctors
is replaced by its ambient space functor.The analytic type of the merged functor is the extension of the two analytic types of the functors. The
red_hom
parameter of the merged functor is the logicaland
of the two correspondingred_hom
parameters (where a forms space is assumed to have it set toTrue
).Two
FormsSpaceFunctor
with different (k,ep) are merged to a correspondingFormsRingFunctor
. Otherwise the corresponding (extended)FormsSpaceFunctor
is returned.A
FormsSpaceFunctor
andFormsRingFunctor
are merged to a corresponding (extended)FormsRingFunctor
.Two
FormsRingFunctors
are merged to the corresponding (extended)FormsRingFunctor
.EXAMPLES:
sage: from sage.modular.modform_hecketriangle.functors import (FormsSpaceFunctor, FormsRingFunctor) sage: functor1 = FormsRingFunctor("mero", group=6, red_hom=True) sage: functor2 = FormsRingFunctor(["quasi", "cusp"], group=6, red_hom=False) sage: functor3 = FormsSpaceFunctor("weak", group=6, k=0, ep=1) sage: functor4 = FormsRingFunctor("mero", group=5, red_hom=True) sage: functor1.merge(functor1) is functor1 True sage: functor1.merge(functor4) is None True sage: functor1.merge(functor2) QuasiMeromorphicModularFormsRingFunctor(n=6) sage: functor1.merge(functor3) MeromorphicModularFormsRingFunctor(n=6, red_hom=True)


class
sage.modular.modform_hecketriangle.functors.
FormsSpaceFunctor
(analytic_type, group, k, ep)¶ Bases:
sage.categories.pushout.ConstructionFunctor
Construction functor for forms spaces.
NOTE:
When the base ring is not a
BaseFacade
the functor is first merged with the ConstantFormsSpaceFunctor. This case occurs in the pushout constructions (when trying to find a common parent between a forms space and a ring which is not aBaseFacade
).
AT
= Analytic Type¶

AnalyticType
¶ alias of
sage.modular.modform_hecketriangle.analytic_type.AnalyticType

merge
(other)¶ Return the merged functor of
self
andother
.It is only possible to merge instances of
FormsSpaceFunctor
andFormsRingFunctor
. Also only if they share the same group. AnFormsSubSpaceFunctors
is replaced by its ambient space functor.The analytic type of the merged functor is the extension of the two analytic types of the functors. The
red_hom
parameter of the merged functor is the logicaland
of the two correspondingred_hom
parameters (where a forms space is assumed to have it set toTrue
).Two
FormsSpaceFunctor
with different (k,ep) are merged to a correspondingFormsRingFunctor
. Otherwise the corresponding (extended)FormsSpaceFunctor
is returned.A
FormsSpaceFunctor
andFormsRingFunctor
are merged to a corresponding (extended)FormsRingFunctor
.Two
FormsRingFunctors
are merged to the corresponding (extended)FormsRingFunctor
.EXAMPLES:
sage: from sage.modular.modform_hecketriangle.functors import (FormsSpaceFunctor, FormsRingFunctor) sage: functor1 = FormsSpaceFunctor("holo", group=5, k=0, ep=1) sage: functor2 = FormsSpaceFunctor(["quasi", "cusp"], group=5, k=10/3, ep=1) sage: functor3 = FormsSpaceFunctor(["quasi", "mero"], group=5, k=0, ep=1) sage: functor4 = FormsRingFunctor("cusp", group=5, red_hom=False) sage: functor5 = FormsSpaceFunctor("holo", group=4, k=0, ep=1) sage: functor1.merge(functor1) is functor1 True sage: functor1.merge(functor5) is None True sage: functor1.merge(functor2) QuasiModularFormsRingFunctor(n=5, red_hom=True) sage: functor1.merge(functor3) QuasiMeromorphicModularFormsFunctor(n=5, k=0, ep=1) sage: functor1.merge(functor4) ModularFormsRingFunctor(n=5)


class
sage.modular.modform_hecketriangle.functors.
FormsSubSpaceFunctor
(ambient_space_functor, generators)¶ Bases:
sage.categories.pushout.ConstructionFunctor
Construction functor for forms sub spaces.

merge
(other)¶ Return the merged functor of
self
andother
.If
other
is aFormsSubSpaceFunctor
then first the common ambient space functor is constructed by merging the two corresponding functors.If that ambient space functor is a FormsSpaceFunctor and the generators agree the corresponding
FormsSubSpaceFunctor
is returned.If
other
is not aFormsSubSpaceFunctor
thenself
is merged as if it was its ambient space functor.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_functor1 = FormsSpaceFunctor("holo", group=4, k=12, ep=1) sage: ambient_space_functor2 = FormsSpaceFunctor("cusp", group=4, k=12, ep=1) sage: ss_functor1 = FormsSubSpaceFunctor(ambient_space_functor1, [ambient_space.gen(0)]) sage: ss_functor2 = FormsSubSpaceFunctor(ambient_space_functor2, [ambient_space.gen(0)]) sage: ss_functor3 = FormsSubSpaceFunctor(ambient_space_functor2, [2*ambient_space.gen(0)]) sage: merged_ambient = ambient_space_functor1.merge(ambient_space_functor2) sage: merged_ambient ModularFormsFunctor(n=4, k=12, ep=1) sage: functor4 = FormsSpaceFunctor(["quasi", "cusp"], group=4, k=10, ep=1) sage: ss_functor1.merge(ss_functor1) is ss_functor1 True sage: ss_functor1.merge(ss_functor2) FormsSubSpaceFunctor with 2 generators for the ModularFormsFunctor(n=4, k=12, ep=1) sage: ss_functor1.merge(ss_functor2) == FormsSubSpaceFunctor(merged_ambient, [ambient_space.gen(0), ambient_space.gen(0)]) True sage: ss_functor1.merge(ss_functor3) == FormsSubSpaceFunctor(merged_ambient, [ambient_space.gen(0), 2*ambient_space.gen(0)]) True sage: ss_functor1.merge(ambient_space_functor2) == merged_ambient True sage: ss_functor1.merge(functor4) QuasiModularFormsRingFunctor(n=4, red_hom=True)
