"""
Constructors for certain modular abelian varieties
AUTHORS:
- William Stein (2007-03)
"""
import weakref
from sage.rings.integer import Integer
from sage.modular.arithgroup.all import is_CongruenceSubgroup, Gamma0
from sage.modular.modsym.space import is_ModularSymbolsSpace
from abvar_newform import ModularAbelianVariety_newform
import sage.modular.modform.element
import abvar
_cache = {}
def _get(key):
"""
Returns the cached abelian variety with given key. This is used
internally by the abelian varieties constructor.
INPUT:
- ``key`` - hashable
EXAMPLE::
sage: sage.modular.abvar.constructor._saved('a', J0(37))
Abelian variety J0(37) of dimension 2
sage: sage.modular.abvar.constructor._get('a')
Abelian variety J0(37) of dimension 2
sage: sage.modular.abvar.constructor._get('b')
Traceback (most recent call last):
...
ValueError: element not in cache
"""
if _cache.has_key(key):
z = _cache[key]()
if z is not None:
return z
raise ValueError, "element not in cache"
def _saved(key, J):
"""
Returns the cached abelian variety with given key. This is used
internally by the abelian varieties constructor.
INPUT:
- ``key`` - hashable
- ``J`` - modular abelian variety
OUTPUT:
- ``J`` - returns the modabvar, to make code that uses
this simpler
EXAMPLES::
sage: sage.modular.abvar.constructor._saved('37', J0(37))
Abelian variety J0(37) of dimension 2
"""
_cache[key] = weakref.ref(J)
return J
def J0(N):
"""
Return the Jacobian `J_0(N)` of the modular curve
`X_0(N)`.
EXAMPLES::
sage: J0(389)
Abelian variety J0(389) of dimension 32
The result is cached::
sage: J0(33) is J0(33)
True
"""
key = 'J0(%s)'%N
try:
return _get(key)
except ValueError:
from sage.modular.arithgroup.all import Gamma0
J = Gamma0(N).modular_abelian_variety()
return _saved(key, J)
def J1(N):
"""
Return the Jacobian `J_1(N)` of the modular curve
`X_1(N)`.
EXAMPLES::
sage: J1(389)
Abelian variety J1(389) of dimension 6112
"""
key = 'J1(%s)'%N
try:
return _get(key)
except ValueError:
from sage.modular.arithgroup.all import Gamma1
return _saved(key, Gamma1(N).modular_abelian_variety())
def JH(N, H):
"""
Return the Jacobian `J_H(N)` of the modular curve
`X_H(N)`.
EXAMPLES::
sage: JH(389,[16])
Abelian variety JH(389,[16]) of dimension 64
"""
key = 'JH(%s,%s)'%(N,H)
try:
return _get(key)
except ValueError:
from sage.modular.arithgroup.all import GammaH
return _saved(key, GammaH(N, H).modular_abelian_variety())
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"
