def endomorphismSpace2(self):
pool.start_pool()
endspace = parallel_weaksim(self.stconsts)
x = endspace.get()
endo = ParallelIntersection(x, packed=True).get()
pool.stop_pool()
return endo
def compute_basis2(As, Bs):
pool.start_pool()
Lspaces = parallel_weaksim(Bs)
Vspaces = parallel_weaksim(As, Bs)
Lbasis = ParallelIntersection(Lspaces.get(), packed=True, nch=pool.PROCESSES/2)
Vbasis = ParallelIntersection(Vspaces.get(), packed=True, nch=pool.PROCESSES/2)
pool.stop_pool()
return (Lbasis.get(), Vbasis.get())
def similarity(As, Bs, name=None):
dim = As[0].row
field = As[0].coeff_ring
for A in As: assert A.row == A.column == dim
for B in Bs: assert B.row == B.column == dim
assert len(As) == len(Bs)
print "Simultaneous similarity over %d %dx%d matrices" % (len(As), dim, dim)
if name is not None:
try:
Vbasis = numpy_load_matrices(
default_file_name(name + "_basis", field), field)
L = algebra.Algebra.fromFile(field, name)
#L.semisimple = True
V = algebra.Module.fromFile(field, L, name)
except IOError:
L = None
V = None
if name is None or L is None or V is None:
(Lbasis, Vbasis) = compute_basis3(As, Bs)
pool.stop_pool()
# If V = {}, then there is no solution.
if not Vbasis:
print "No X found such that X*A_i = B_i*X"
return None
assert all([X * B == B * X for B in Bs for X in Lbasis])
assert all([X * A == B * X for (A, B) in zip(As, Bs) for X in Vbasis])
print "Constructing %d-dimensional algebra L" % len(Lbasis)
L = algebra.Algebra.fromBasis(field, Lbasis)
#L.semisimple = True
print "Constructing %d-dimensional module V" % len(Vbasis)
V = algebra.Module.fromBasis(field, Lbasis, Vbasis, L)
if name is not None:
# Save this work for later.
L.save(name)
V.save(name)
numpy_save_matrices(Vbasis, default_file_name(name + "_basis", field))
#print_matrices(V.stconsts)
print "Finding a generator in V"
v = V.findGenerator()
if v is not None:
Z = vector_to_matrix(v, Vbasis)
# Check if Z is invertible, i.e. if v is a unit. If v is not a unit
# then there are no units in V.
try:
Zprime = Z.inverse()
except matrix.NoInverse:
return None
assert all(Z * A * Zprime == B for (A,B) in zip(As, Bs))
return Z
return None
