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 Integer(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
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 Integer(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
else:
del Q
del N
return False