def is_quotient(M,sym,rank):
symbol=GenusSymbol_global_ring(MatrixSpace(ZZ,rank,rank).one())
symbol._local_symbols=[Genus_Symbol_p_adic_ring(p,syms) for p,syms in sym.iteritems()]
s = get_symbol_string(symbol)
print s
N = FiniteQuadraticModule(s)
t = N.order()/M.order()
if not Integer(t).is_square():
return False
else:
t = sqrt(t)
for p in N.order().prime_factors():
if not N.signature(p) == M.signature(p):
return False
#if not N.signature() == M.signature():
# return False
for G in N.subgroups():
if G.order() == t and G.is_isotropic():
Q = G.quotient()
if Q.is_isomorphic(M):
print Q
return N.jordan_decomposition().genus_symbol()
else:
del(Q)
del(N)
return False
def is_quotient(M, sym, rank):
symbol = GenusSymbol_global_ring(MatrixSpace(ZZ, rank, rank).one())
symbol._local_symbols = [
Genus_Symbol_p_adic_ring(p, syms) for p, syms in sym.iteritems()
]
s = get_symbol_string(symbol)
print s
N = FiniteQuadraticModule(s)
t = N.order() / M.order()
if not Integer(t).is_square():
return False
else:
t = sqrt(t)
for p in N.order().prime_factors():
if not N.signature(p) == M.signature(p):
return False
#if not N.signature() == M.signature():
# return False
for G in N.subgroups():
if G.order() == t and G.is_isotropic():
Q = G.quotient()
if Q.is_isomorphic(M):
print Q
return N.jordan_decomposition().genus_symbol()
else:
del (Q)
del (N)
return False
def weight_one_half_dim(FQM,
use_reduction=True,
proof=False,
debug=0,
local=True):
N = Integer(FQM.level())
if not N % 4 == 0:
return 0
m = Integer(N / Integer(4))
d = 0
for l in m.divisors():
if is_squarefree(m / l):
if debug > 1: print "l = {0}".format(l)
TM = FiniteQuadraticModule([2 * l], [-1 / Integer(4 * l)])
if local:
dd = [0, 0] # eigenvalue 1, -1 multiplicity
for p, n in lcm(FQM.level(), 4 * l).factor():
N = None
TN = None
J = FQM.jordan_decomposition()
L = TM.jordan_decomposition()
for j in xrange(1, n + 1):
C = J.constituent(p**j)[0]
D = L.constituent(p**j)[0]
if debug > 1: print "C = {0}, D = {1}".format(C, D)
if N == None and C.level() != 1:
N = C
elif C.level() != 1:
N = N + C
if TN == None and D.level() != 1:
TN = D
elif D.level() != 1:
TN = TN + D
dd1 = invariants_eps(N, TN, use_reduction, proof, debug)
if debug > 1: print "dd1 = {}".format(dd1)
if dd1 == [0, 0]:
# the result is multiplicative
# a single [0,0] as a local result
# yields [0,0] in the end
# and we're done here
dd = [0, 0]
break
if dd == [0, 0]:
# this is the first prime
dd = dd1
else:
# some basic arithmetic ;-)
# 1 = 1*1 = (-1)(-1)
# -1 = 1*(-1) = (-1)*1
ddtmp = copy(dd)
ddtmp[0] = dd[0] * dd1[0] + dd[1] * dd1[1]
ddtmp[1] = dd[0] * dd1[1] + dd[1] * dd1[0]
dd = ddtmp
if debug > 1: print "dd = {0}".format(dd)
d += dd[0]
else:
d += invariants_eps(FQM, TM, use_reduction, proof, debug)[0]
return d
def weight_one_half_dim(FQM, use_reduction = True, proof = False, debug = 0, local=True):
N = Integer(FQM.level())
if not N % 4 == 0:
return 0
m = Integer(N/Integer(4))
d = 0
for l in m.divisors():
if is_squarefree(m/l):
if debug > 1: print "l = {0}".format(l)
TM = FiniteQuadraticModule([2*l],[-1/Integer(4*l)])
if local:
dd = [0,0] # eigenvalue 1, -1 multiplicity
for p,n in lcm(FQM.level(),4*l).factor():
N = None
TN = None
J = FQM.jordan_decomposition()
L = TM.jordan_decomposition()
for j in xrange(1,n+1):
C = J.constituent(p**j)[0]
D = L.constituent(p**j)[0]
if debug > 1: print "C = {0}, D = {1}".format(C,D)
if N == None and C.level() != 1:
N = C
elif C.level() != 1:
N = N + C
if TN == None and D.level() != 1:
TN = D
elif D.level() != 1:
TN = TN + D
dd1 = invariants_eps(N, TN, use_reduction, proof, debug)
if debug > 1: print "dd1 = {}".format(dd1)
if dd1 == [0,0]:
# the result is multiplicative
# a single [0,0] as a local result
# yields [0,0] in the end
# and we're done here
dd = [0,0]
break
if dd == [0,0]:
# this is the first prime
dd = dd1
else:
# some basic arithmetic ;-)
# 1 = 1*1 = (-1)(-1)
# -1 = 1*(-1) = (-1)*1
ddtmp = copy(dd)
ddtmp[0] = dd[0]*dd1[0] + dd[1]*dd1[1]
ddtmp[1] = dd[0]*dd1[1] + dd[1]*dd1[0]
dd = ddtmp
if debug > 1: print "dd = {0}".format(dd)
d += dd[0]
else:
d += invariants_eps(FQM, TM, use_reduction, proof, debug)[0]
return d
def test_dimension_jacobi(N, k):
from nils.jacobiforms.dimension_jac_forms import dimension_jac_cusp_forms
N = Integer(N)
dj = dimension_jac_cusp_forms(k + Integer(1) / Integer(2), N)
M = FiniteQuadraticModule([2 * N], [1 / (4 * N)])
s = GenusSymbol(M.jordan_decomposition().genus_symbol())
dv = s.dimension_cusp_forms(k, reduction=True)
if not dj == dv:
print "Error: ", N, dj, dv
return False
return True
def test_dimension_jacobi(N, k):
from nils.jacobiforms.dimension_jac_forms import dimension_jac_cusp_forms
N = Integer(N)
dj = dimension_jac_cusp_forms(k + Integer(1) / Integer(2), N)
M = FiniteQuadraticModule([2 * N], [1 / (4 * N)])
s = GenusSymbol(M.jordan_decomposition().genus_symbol())
dv = s.dimension_cusp_forms(k, reduction=True)
if not dj == dv:
print "Error: ", N, dj, dv
return False
return True
def compute_simple_shimura_curves(path=''):
l = load(path + '/lattices_aniso_1_notgamma0.sobj')
simshim = []
aniso_shim_syms=[]
for Q in l:
M = FiniteQuadraticModule(Q.matrix())
s = GenusSymbol(M.jordan_decomposition().genus_symbol())
aniso_shim_syms.append(s)
G = SimpleModulesGraph2n(1,None)
G.compute_from_startpoints(aniso_shim_syms)
simshim.extend(G._simple)
return simshim
def compute_simple_shimura_curves(path=''):
l = load(path + '/lattices_aniso_1_notgamma0.sobj')
simshim = []
aniso_shim_syms = []
for Q in l:
M = FiniteQuadraticModule(Q.matrix())
s = GenusSymbol(M.jordan_decomposition().genus_symbol())
aniso_shim_syms.append(s)
G = SimpleModulesGraph2n(1, None)
G.compute_from_startpoints(aniso_shim_syms)
simshim.extend(G._simple)
return simshim
def Bbf(M, m): # brute force algorithm
if isinstance(M, str):
M = FiniteQuadraticModule(M)
rank = len(M.gens()) + 2
sign = M.signature()
symbols = all_symbols(sign, rank, M.order() * m ** 2)
B = list(is_quotient([(M, sym, rank) for sym in symbols]))
B = filter(lambda x: x[1] != False, B)
B = map(lambda x: x[1], B)
modules = Set(B)
modules_unique = list()
for M in modules:
seen = False
for N in modules_unique:
if N.is_isomorphic(M):
seen = True
if not seen:
modules_unique.append(M)
return [M.jordan_decomposition().genus_symbol() for M in modules_unique]
def Bbf(M, m): # brute force algorithm
if isinstance(M, str):
M = FiniteQuadraticModule(M)
rank = len(M.gens()) + 2
sign = M.signature()
symbols = all_symbols(sign, rank, M.order() * m**2)
B = list(is_quotient([(M, sym, rank) for sym in symbols]))
B = filter(lambda x: x[1] != False, B)
B = map(lambda x: x[1], B)
modules = Set(B)
modules_unique = list()
for M in modules:
seen = False
for N in modules_unique:
if N.is_isomorphic(M):
seen = True
if not seen:
modules_unique.append(M)
return [M.jordan_decomposition().genus_symbol() for M in modules_unique]
