def AbelianVariety(X):
"""
Create the abelian variety corresponding to the given defining
data.
INPUT:
- ``X`` - an integer, string, newform, modsym space,
congruence subgroup or tuple of congruence subgroups
OUTPUT: a modular abelian variety
EXAMPLES::
sage: AbelianVariety(Gamma0(37))
Abelian variety J0(37) of dimension 2
sage: AbelianVariety('37a')
Newform abelian subvariety 37a of dimension 1 of J0(37)
sage: AbelianVariety(Newform('37a'))
Newform abelian subvariety 37a of dimension 1 of J0(37)
sage: AbelianVariety(ModularSymbols(37).cuspidal_submodule())
Abelian variety J0(37) of dimension 2
sage: AbelianVariety((Gamma0(37), Gamma0(11)))
Abelian variety J0(37) x J0(11) of dimension 3
sage: AbelianVariety(37)
Abelian variety J0(37) of dimension 2
sage: AbelianVariety([1,2,3])
Traceback (most recent call last):
...
TypeError: X must be an integer, string, newform, modsym space, congruence subgroup or tuple of congruence subgroups
"""
if isinstance(X, (int, long, Integer)):
X = Gamma0(X)
if is_CongruenceSubgroup(X):
X = X.modular_symbols().cuspidal_submodule()
elif isinstance(X, str):
from sage.modular.modform.constructor import Newform
f = Newform(X, names='a')
return ModularAbelianVariety_newform(f, internal_name=True)
elif isinstance(X, sage.modular.modform.element.Newform):
return ModularAbelianVariety_newform(X)
if is_ModularSymbolsSpace(X):
return abvar.ModularAbelianVariety_modsym(X)
if isinstance(X,
(tuple, list)) and all([is_CongruenceSubgroup(G)
for G in X]):
return abvar.ModularAbelianVariety(X)
raise TypeError(
"X must be an integer, string, newform, modsym space, congruence subgroup or tuple of congruence subgroups"
)
def AbelianVariety(X):
"""
Create the abelian variety corresponding to the given defining
data.
INPUT:
- ``X`` - an integer, string, newform, modsym space,
congruence subgroup or tuple of congruence subgroups
OUTPUT: a modular abelian variety
EXAMPLES::
sage: AbelianVariety(Gamma0(37))
Abelian variety J0(37) of dimension 2
sage: AbelianVariety('37a')
Newform abelian subvariety 37a of dimension 1 of J0(37)
sage: AbelianVariety(Newform('37a'))
Newform abelian subvariety 37a of dimension 1 of J0(37)
sage: AbelianVariety(ModularSymbols(37).cuspidal_submodule())
Abelian variety J0(37) of dimension 2
sage: AbelianVariety((Gamma0(37), Gamma0(11)))
Abelian variety J0(37) x J0(11) of dimension 3
sage: AbelianVariety(37)
Abelian variety J0(37) of dimension 2
sage: AbelianVariety([1,2,3])
Traceback (most recent call last):
...
TypeError: X must be an integer, string, newform, modsym space, congruence subgroup or tuple of congruence subgroups
"""
if isinstance(X, (int, long, Integer)):
X = Gamma0(X)
if is_CongruenceSubgroup(X):
X = X.modular_symbols().cuspidal_submodule()
elif isinstance(X, str):
from sage.modular.modform.constructor import Newform
f = Newform(X, names='a')
return ModularAbelianVariety_newform(f, internal_name=True)
elif isinstance(X, sage.modular.modform.element.Newform):
return ModularAbelianVariety_newform(X)
if is_ModularSymbolsSpace(X):
return abvar.ModularAbelianVariety_modsym(X)
if isinstance(X, (tuple,list)) and all([is_CongruenceSubgroup(G) for G in X]):
return abvar.ModularAbelianVariety(X)
raise TypeError("X must be an integer, string, newform, modsym space, congruence subgroup or tuple of congruence subgroups")