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r""" 

Functor construction for all spaces 

 

AUTHORS: 

 

- Jonas Jermann (2013): initial version 

 

""" 

from __future__ import absolute_import 

 

#***************************************************************************** 

# Copyright (C) 2013-2014 Jonas Jermann <jjermann2@gmail.com> 

# 

# Distributed under the terms of the GNU General Public License (GPL) 

# as published by the Free Software Foundation; either version 2 of 

# the License, or (at your option) any later version. 

# http://www.gnu.org/licenses/ 

#***************************************************************************** 

 

from sage.rings.all import ZZ, QQ, infinity 

 

from sage.categories.functor import Functor 

from sage.categories.pushout import ConstructionFunctor 

from sage.categories.sets_cat import Sets 

from sage.structure.parent import Parent 

from sage.categories.commutative_additive_groups import CommutativeAdditiveGroups 

from sage.categories.rings import Rings 

 

from .constructor import FormsSpace, FormsRing 

from .abstract_space import FormsSpace_abstract 

from .subspace import SubSpaceForms 

 

 

def _get_base_ring(ring, var_name="d"): 

r""" 

Return the base ring of the given ``ring``: 

 

If ``ring`` is of the form ``FractionField(PolynomialRing(R,'d'))``: 

Return ``R``. 

 

If ``ring`` is of the form ``FractionField(R)``: 

Return ``R``. 

 

If ``ring`` is of the form ``PolynomialRing(R,'d')``: 

Return ``R``. 

 

Otherwise return ``ring``. 

 

The base ring is used in the construction of the corresponding 

``FormsRing`` or ``FormsSpace``. In particular in the construction 

of holomorphic forms of degree (0, 1). For (binary) 

operations a general ring element is considered (coerced to) 

a (constant) holomorphic form of degree (0, 1) 

whose construction should be based on the returned base ring 

(and not on ``ring``!). 

 

If ``var_name`` (default: "d") is specified then this variable 

name is used for the polynomial ring. 

 

EXAMPLES:: 

 

sage: from sage.modular.modform_hecketriangle.functors import _get_base_ring 

sage: _get_base_ring(ZZ) == ZZ 

True 

sage: _get_base_ring(QQ) == ZZ 

True 

sage: _get_base_ring(PolynomialRing(CC, 'd')) == CC 

True 

sage: _get_base_ring(PolynomialRing(QQ, 'd')) == ZZ 

True 

sage: _get_base_ring(FractionField(PolynomialRing(CC, 'd'))) == CC 

True 

sage: _get_base_ring(FractionField(PolynomialRing(QQ, 'd'))) == ZZ 

True 

sage: _get_base_ring(PolynomialRing(QQ, 'x')) == PolynomialRing(QQ, 'x') 

True 

""" 

 

#from sage.rings.fraction_field import is_FractionField 

from sage.rings.polynomial.polynomial_ring import is_PolynomialRing 

from sage.categories.pushout import FractionField as FractionFieldFunctor 

 

base_ring = ring 

#if (is_FractionField(base_ring)): 

# base_ring = base_ring.base() 

if (base_ring.construction() and base_ring.construction()[0] == FractionFieldFunctor()): 

base_ring = base_ring.construction()[1] 

if (is_PolynomialRing(base_ring) and base_ring.ngens()==1 and base_ring.variable_name()==var_name): 

base_ring = base_ring.base() 

if (base_ring.construction() and base_ring.construction()[0] == FractionFieldFunctor()): 

base_ring = base_ring.construction()[1] 

 

return base_ring 

 

 

def _common_subgroup(group1, group2): 

r""" 

Return a common (Hecke triangle) subgroup of both given groups 

``group1`` and ``group2`` if it exists. Otherwise return ``None``. 

 

EXAMPLES:: 

 

sage: from sage.modular.modform_hecketriangle.functors import _common_subgroup 

sage: from sage.modular.modform_hecketriangle.hecke_triangle_groups import HeckeTriangleGroup 

sage: _common_subgroup(HeckeTriangleGroup(n=3), HeckeTriangleGroup(n=infinity)) 

Hecke triangle group for n = +Infinity 

sage: _common_subgroup(HeckeTriangleGroup(n=infinity), HeckeTriangleGroup(n=3)) 

Hecke triangle group for n = +Infinity 

sage: _common_subgroup(HeckeTriangleGroup(n=4), HeckeTriangleGroup(n=infinity)) is None 

True 

sage: _common_subgroup(HeckeTriangleGroup(n=4), HeckeTriangleGroup(n=4)) 

Hecke triangle group for n = 4 

""" 

 

if group1 == group2: 

return group1 

elif (group1.n() == 3) and (group2.n() == infinity): 

return group2 

elif (group1.n() == infinity) and (group2.n() == 3): 

return group1 

else: 

return None 

 

 

def ConstantFormsSpaceFunctor(group): 

r""" 

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) 

""" 

return FormsSpaceFunctor("holo", group, QQ.zero(), ZZ.one()) 

 

 

class FormsSubSpaceFunctor(ConstructionFunctor): 

r""" 

Construction functor for forms sub spaces. 

""" 

 

rank = 10 

 

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 __call__(self, R): 

r""" 

Return the corresponding subspace of the ambient space 

constructed by ``self._ambient_space`` with the generators ``self._generators``. 

If the ambient space is not a forms space the ambient space is returned. 

 

EXAMPLES:: 

 

sage: from sage.modular.modform_hecketriangle.functors import (FormsSpaceFunctor, FormsSubSpaceFunctor, BaseFacade) 

sage: from sage.modular.modform_hecketriangle.space import CuspForms 

sage: ambient_space = CuspForms(n=4, k=12, ep=1) 

sage: ambient_space_functor = FormsSpaceFunctor("cusp", group=4, k=12, ep=1) 

sage: el = ambient_space.gen(0) 

sage: F = FormsSubSpaceFunctor(ambient_space_functor, [el]) 

sage: F 

FormsSubSpaceFunctor with 1 generator for the CuspFormsFunctor(n=4, k=12, ep=1) 

 

sage: F(BaseFacade(ZZ)) 

Subspace of dimension 1 of CuspForms(n=4, k=12, ep=1) over Integer Ring 

sage: F(BaseFacade(CC)) 

Subspace of dimension 1 of CuspForms(n=4, k=12, ep=1) over Complex Field with 53 bits of precision 

sage: F(CC) 

ModularFormsRing(n=4) over Complex Field with 53 bits of precision 

 

sage: ambient_space_functor = FormsSpaceFunctor("holo", group=4, k=0, ep=1) 

sage: F = FormsSubSpaceFunctor(ambient_space_functor, [1]) 

sage: F 

FormsSubSpaceFunctor with 1 generator for the ModularFormsFunctor(n=4, k=0, ep=1) 

sage: F(BaseFacade(ZZ)) 

Subspace of dimension 1 of ModularForms(n=4, k=0, ep=1) over Integer Ring 

sage: F(CC) 

Subspace of dimension 1 of ModularForms(n=4, k=0, ep=1) over Complex Field with 53 bits of precision 

""" 

 

ambient_space = self._ambient_space_functor(R) 

if isinstance(ambient_space, FormsSpace_abstract): 

return SubSpaceForms(ambient_space, self._generators) 

else: 

return ambient_space 

 

def _repr_(self): 

r""" 

Return the string representation of ``self``. 

 

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: FormsSubSpaceFunctor(ambient_space_functor, ambient_space.gens()) 

FormsSubSpaceFunctor with 2 generators for the ModularFormsFunctor(n=4, k=12, ep=1) 

sage: FormsSubSpaceFunctor(ambient_space_functor, [ambient_space.gen(0)]) 

FormsSubSpaceFunctor with 1 generator for the ModularFormsFunctor(n=4, k=12, ep=1) 

""" 

 

return "FormsSubSpaceFunctor with {} generator{} for the {}".format(len(self._generators), 's' if len(self._generators) != 1 else '', self._ambient_space_functor) 

 

def merge(self, other): 

r""" 

Return the merged functor of ``self`` and ``other``. 

 

If ``other`` is a ``FormsSubSpaceFunctor`` 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 a ``FormsSubSpaceFunctor`` then ``self`` 

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) 

""" 

 

if (self == other): 

return self 

elif isinstance(other, FormsSubSpaceFunctor): 

merged_ambient_space_functor = self._ambient_space_functor.merge(other._ambient_space_functor) 

if isinstance(merged_ambient_space_functor, FormsSpaceFunctor): 

generators = self._generators + other._generators 

return FormsSubSpaceFunctor(merged_ambient_space_functor, generators) 

# This includes the case when None is returned 

else: 

return merged_ambient_space_functor 

else: 

return self._ambient_space_functor.merge(other) 

 

def __eq__(self, other): 

r""" 

Compare ``self`` and ``other``. 

 

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: ss_functor1 = FormsSubSpaceFunctor(ambient_space_functor1, [ambient_space.gen(0)]) 

sage: ss_functor2 = FormsSubSpaceFunctor(ambient_space_functor1, [ambient_space.gen(1)]) 

sage: ss_functor1 == ss_functor2 

False 

""" 

 

if (type(self) is type(other) and 

self._ambient_space_functor == other._ambient_space_functor and 

self._generators == other._generators): 

return True 

else: 

return False 

 

 

class FormsSpaceFunctor(ConstructionFunctor): 

r""" 

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 a ``BaseFacade``). 

""" 

 

from .analytic_type import AnalyticType 

AT = AnalyticType() 

 

rank = 10 

 

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 __call__(self, R): 

r""" 

If ``R`` is a ``BaseFacade(S)`` then return the corresponding 

forms space with base ring ``_get_base_ring(S)``. 

 

If not then we first merge the functor with the ConstantFormsSpaceFunctor. 

 

EXAMPLES:: 

 

sage: from sage.modular.modform_hecketriangle.functors import (FormsSpaceFunctor, BaseFacade) 

sage: F = FormsSpaceFunctor(["holo", "weak"], group=4, k=0, ep=-1) 

sage: F(BaseFacade(ZZ)) 

WeakModularForms(n=4, k=0, ep=-1) over Integer Ring 

sage: F(BaseFacade(CC)) 

WeakModularForms(n=4, k=0, ep=-1) over Complex Field with 53 bits of precision 

sage: F(CC) 

WeakModularFormsRing(n=4) over Complex Field with 53 bits of precision 

sage: F(CC).has_reduce_hom() 

True 

""" 

 

if (isinstance(R, BaseFacade)): 

R = _get_base_ring(R._ring) 

return FormsSpace(self._analytic_type, self._group, R, self._k, self._ep) 

else: 

R = BaseFacade(_get_base_ring(R)) 

merged_functor = self.merge(ConstantFormsSpaceFunctor(self._group)) 

return merged_functor(R) 

 

def _repr_(self): 

r""" 

Return the string representation of ``self``. 

 

EXAMPLES:: 

 

sage: from sage.modular.modform_hecketriangle.functors import FormsSpaceFunctor 

sage: F = FormsSpaceFunctor(["cusp", "quasi"], group=5, k=10/3, ep=-1) 

sage: str(F) 

'QuasiCuspFormsFunctor(n=5, k=10/3, ep=-1)' 

sage: F 

QuasiCuspFormsFunctor(n=5, k=10/3, ep=-1) 

""" 

 

return "{}FormsFunctor(n={}, k={}, ep={})".format(self._analytic_type.analytic_space_name(), self._group.n(), self._k, self._ep) 

 

def merge(self, other): 

r""" 

Return the merged functor of ``self`` and ``other``. 

 

It is only possible to merge instances of ``FormsSpaceFunctor`` 

and ``FormsRingFunctor``. Also only if they share the same group. 

An ``FormsSubSpaceFunctors`` 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 logical ``and`` of the two corresponding ``red_hom`` 

parameters (where a forms space is assumed to have it 

set to ``True``). 

 

Two ``FormsSpaceFunctor`` with different (k,ep) are merged to a 

corresponding ``FormsRingFunctor``. Otherwise the corresponding 

(extended) ``FormsSpaceFunctor`` is returned. 

 

A ``FormsSpaceFunctor`` and ``FormsRingFunctor`` 

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) 

""" 

 

if (self == other): 

return self 

 

if isinstance(other, FormsSubSpaceFunctor): 

other = other._ambient_space_functor 

 

if isinstance(other, FormsSpaceFunctor): 

group = _common_subgroup(self._group, other._group) 

if group is None: 

return None 

analytic_type = self._analytic_type + other._analytic_type 

if (self._k == other._k) and (self._ep == other._ep): 

return FormsSpaceFunctor(analytic_type, group, self._k, self._ep) 

else: 

return FormsRingFunctor(analytic_type, group, True) 

elif isinstance(other, FormsRingFunctor): 

group = _common_subgroup(self._group, other._group) 

if group is None: 

return None 

red_hom = other._red_hom 

analytic_type = self._analytic_type + other._analytic_type 

return FormsRingFunctor(analytic_type, group, red_hom) 

 

def __eq__(self, other): 

r""" 

Compare ``self`` and ``other``. 

 

EXAMPLES:: 

 

sage: from sage.modular.modform_hecketriangle.functors import FormsSpaceFunctor 

sage: functor1 = FormsSpaceFunctor("holo", group=4, k=12, ep=1) 

sage: functor2 = FormsSpaceFunctor("holo", group=4, k=12, ep=-1) 

sage: functor1 == functor2 

False 

""" 

 

if (type(self) is type(other) and 

self._group == other._group and 

self._analytic_type == other._analytic_type and 

self._k == other._k and 

self._ep == other._ep): 

return True 

else: 

return False 

 

 

class FormsRingFunctor(ConstructionFunctor): 

r""" 

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 a ``BaseFacade``). 

""" 

 

from .analytic_type import AnalyticType 

AT = AnalyticType() 

 

rank = 10 

 

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 __call__(self, R): 

r""" 

If ``R`` is a ``BaseFacade(S)`` then return the corresponding 

forms ring with base ring ``_get_base_ring(S)``. 

 

If not then we first merge the functor with the ConstantFormsSpaceFunctor. 

 

EXAMPLES:: 

 

sage: from sage.modular.modform_hecketriangle.functors import (FormsRingFunctor, BaseFacade) 

sage: F = FormsRingFunctor(["quasi", "mero"], group=6, red_hom=False) 

sage: F(BaseFacade(ZZ)) 

QuasiMeromorphicModularFormsRing(n=6) over Integer Ring 

sage: F(BaseFacade(CC)) 

QuasiMeromorphicModularFormsRing(n=6) over Complex Field with 53 bits of precision 

sage: F(CC) 

QuasiMeromorphicModularFormsRing(n=6) over Complex Field with 53 bits of precision 

sage: F(CC).has_reduce_hom() 

False 

""" 

 

if (isinstance(R, BaseFacade)): 

R = _get_base_ring(R._ring) 

return FormsRing(self._analytic_type, self._group, R, self._red_hom) 

else: 

R = BaseFacade(_get_base_ring(R)) 

merged_functor = self.merge(ConstantFormsSpaceFunctor(self._group)) 

return merged_functor(R) 

 

def _repr_(self): 

r""" 

Return the string representation of ``self``. 

 

EXAMPLES:: 

 

sage: from sage.modular.modform_hecketriangle.functors import FormsRingFunctor 

sage: str(FormsRingFunctor(["quasi", "mero"], group=6, red_hom=True)) 

'QuasiMeromorphicModularFormsRingFunctor(n=6, red_hom=True)' 

sage: FormsRingFunctor(["quasi", "mero"], group=6, red_hom=False) 

QuasiMeromorphicModularFormsRingFunctor(n=6) 

""" 

 

if (self._red_hom): 

red_arg = ", red_hom=True" 

else: 

red_arg = "" 

return "{}FormsRingFunctor(n={}{})".format(self._analytic_type.analytic_space_name(), self._group.n(), red_arg) 

 

def merge(self, other): 

r""" 

Return the merged functor of ``self`` and ``other``. 

 

It is only possible to merge instances of ``FormsSpaceFunctor`` 

and ``FormsRingFunctor``. Also only if they share the same group. 

An ``FormsSubSpaceFunctors`` 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 logical ``and`` of the two corresponding ``red_hom`` 

parameters (where a forms space is assumed to have it 

set to ``True``). 

 

Two ``FormsSpaceFunctor`` with different (k,ep) are merged to a 

corresponding ``FormsRingFunctor``. Otherwise the corresponding 

(extended) ``FormsSpaceFunctor`` is returned. 

 

A ``FormsSpaceFunctor`` and ``FormsRingFunctor`` 

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) 

""" 

 

if (self == other): 

return self 

 

if isinstance(other, FormsSubSpaceFunctor): 

other = other._ambient_space_functor 

 

if isinstance(other, FormsSpaceFunctor): 

group = _common_subgroup(self._group, other._group) 

if group is None: 

return None 

red_hom = self._red_hom 

analytic_type = self._analytic_type + other._analytic_type 

return FormsRingFunctor(analytic_type, group, red_hom) 

elif isinstance(other, FormsRingFunctor): 

group = _common_subgroup(self._group, other._group) 

if group is None: 

return None 

red_hom = self._red_hom & other._red_hom 

analytic_type = self._analytic_type + other._analytic_type 

return FormsRingFunctor(analytic_type, group, red_hom) 

 

def __eq__(self, other): 

r""" 

Compare ``self`` and ``other``. 

 

EXAMPLES:: 

 

sage: from sage.modular.modform_hecketriangle.functors import FormsRingFunctor 

sage: functor1 = FormsRingFunctor("holo", group=4, red_hom=True) 

sage: functor2 = FormsRingFunctor("holo", group=4, red_hom=False) 

sage: functor1 == functor2 

False 

""" 

 

if (type(self) is type(other) and 

self._group == other._group and 

self._analytic_type == other._analytic_type and 

self._red_hom == other._red_hom): 

return True 

else: 

return False 

 

 

from sage.structure.unique_representation import UniqueRepresentation 

class BaseFacade(Parent, UniqueRepresentation): 

r""" 

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`` or ``FormsSpace`` 

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 the ``FormsSpace`` over the ring. However 

this is not correct, the ``FormsSpace`` might 

(and probably will) not even contain the (constant) 

ring element. Hence we use the ``BaseFacade`` 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 the ``BaseFacade`` of it). 

""" 

 

def __init__(self, ring): 

r""" 

BaseFacade of ``ring`` (see above). 

 

EXAMPLES:: 

 

sage: from sage.modular.modform_hecketriangle.functors import BaseFacade 

sage: BaseFacade(ZZ) 

BaseFacade(Integer Ring) 

sage: ZZ.has_coerce_map_from(BaseFacade(ZZ)) 

True 

sage: CC.has_coerce_map_from(BaseFacade(ZZ)) 

True 

""" 

 

Parent.__init__(self, facade=ring, category=Rings()) 

self._ring = _get_base_ring(ring) 

# The BaseFacade(R) coerces/embeds into R, used in pushout 

self.register_embedding(self.Hom(self._ring,Sets())(lambda x: x)) 

 

def __repr__(self): 

r""" 

Return the string representation of ``self``. 

 

EXAMPLES:: 

 

sage: from sage.modular.modform_hecketriangle.functors import BaseFacade 

sage: BaseFacade(ZZ) 

BaseFacade(Integer Ring) 

""" 

 

return "BaseFacade({})".format(self._ring)