def basis_to_ker_basis(self):
C = ModMatrix(self.get_extended_ker_basis())
C.transpose()
inv = C.get_inverse()
if not inv:
raise TypeError("the matrix is not invertible! Something went very wrong")
return inv
def cohom_test(x,y,z,n):
for i in range(n):
AA = ModMatrix.random(y,z)
BB = ModMatrix.random(x,y)
if (BB * AA).is_zero():
print"BB\n", BB, "\n"
print "AA\n", AA, "\n"
coh = Cohomology(BB, AA)
print coh.get_cohomology()
def cohom_test(x, y, z, n):
for i in range(n):
AA = ModMatrix.random(y, z)
BB = ModMatrix.random(x, y)
if (BB * AA).is_zero():
print "BB\n", BB, "\n"
print "AA\n", AA, "\n"
coh = Cohomology(BB, AA)
print coh.get_cohomology()
def matrix_add(i, j, n):
for a in range(n):
xx = ModMatrix.random(i, j)
yy = ModMatrix.random(i, j)
print xx, "\n", yy, "\n", xx + yy, "\n"
xx = ModMatrix.random(i, j)
yy = ModMatrix.random(i + 1, j + 1)
try:
print xx + yy
except TypeError:
print xx, "\n", "wrong size", "\n", yy
def matrix_add(i, j, n):
for a in range(n):
xx = ModMatrix.random(i, j)
yy = ModMatrix.random(i, j)
print xx, "\n", yy, "\n", xx + yy, "\n"
xx = ModMatrix.random(i, j)
yy = ModMatrix.random(i+1, j+1)
try:
print xx + yy
except TypeError:
print xx, "\n", "wrong size", "\n", yy
def extend_ker_basis(self):
ker_basis = self.get_kernel().get_basis()
#assuming vectors are bit vectors
if not ker_basis:
C = ModMatrix.null(1, self.B.col_count)
else:
C = ModMatrix(ker_basis)
comp = C.complement_row_space()
tot = ker_basis[:] + comp[:]
self.extended_ker_basis = tot
self.extended_ker_basis_flag = True
def solve_test(x, y, n):
for i in range(n):
AA = ModMatrix.random(x, y)
bb = ModVector.random(x)
print AA.can_solve(bb)
xx = AA.solve(bb)
print "A\n", AA, "\n"
print "rrefA\n", AA.get_rref(), "\n"
print "b\n", bb, "\n"
print "x\n", xx, "\n"
print "Ax\n", AA * xx
print AA * xx == ModMatrix([bb]).get_transpose()
def append_test(x,y,n):
for i in range(n):
AA = ModMatrix.random(x,y)
zz = ModVector.random(x)
print "AA\n", AA, "\n"
print "zz\n", zz, "\n"
print "append\n", AA.get_append_columns([zz,zz + zz]), "\n"
def inv_test(x,n):
for i in range(n):
AA = ModMatrix.random(x,x)
print "AA\n", AA, "\n"
print "inv\n", AA.get_inverse(), "\n"
if AA.get_inverse():
print "Ix\n", AA * AA.get_inverse(), "\n"
def inv_test(x, n):
for i in range(n):
AA = ModMatrix.random(x, x)
print "AA\n", AA, "\n"
print "inv\n", AA.get_inverse(), "\n"
if AA.get_inverse():
print "Ix\n", AA * AA.get_inverse(), "\n"
def append_test(x, y, n):
for i in range(n):
AA = ModMatrix.random(x, y)
zz = ModVector.random(x)
print "AA\n", AA, "\n"
print "zz\n", zz, "\n"
print "append\n", AA.get_append_columns([zz, zz + zz]), "\n"
def ker_test(x,y,n):
for i in range(n):
AA = ModMatrix.random(x,y)
print AA.get_rref(), "\n"
ker = AA.get_kernel()
for xx in ker:
print "soln\n", xx, "\n"
print "result\n", AA * xx
def ker_test(x, y, n):
for i in range(n):
AA = ModMatrix.random(x, y)
print AA.get_rref(), "\n"
ker = AA.get_kernel()
for xx in ker:
print "soln\n", xx, "\n"
print "result\n", AA * xx
def make_map(self, i):
"""
make matrices in all given bidegrees
this needs a map defined on CobarMonomial objects
does this handle 0 dim vector spaces?
this is a huge timesink. try to do multiprocessing,
check methods for too much simplification
"""
dom = self.get_cplx()[i]
rng = self.get_cplx()[i+1]
for bideg in dom._dict.keys():
out = []
dom_basis = dom._dict[bideg]
cols = len(dom_basis)
try:
rng_basis = rng._dict[bideg]
rows = len(rng_basis)
except KeyError:
rng._dict[bideg] = []
rows = 0
if cols == 0:
# we must account for this later!
cols = 1
#print "bideg in make maps",bideg
dom._maps[bideg] = ModMatrix.null(1,cols)
continue
if cols == 0:
cols = 1
if rows == 0:
rows = 1
#print "bideg in make maps. somethings 0", bideg
dom._maps[bideg] = ModMatrix.null(rows, cols)
continue
for mon in dom_basis:
value = mon._map_reduced()
vect = self.vector_from_element(value, i+1, bideg[0],
bideg[1])
out.append(vect)
matrix = ModMatrix(out).get_transpose()
print " Made matrix: i, bideg, size", i, bideg, matrix.get_size()
dom._maps[bideg] = matrix
def make_map(self, i):
"""
make matrices in all given bidegrees
this needs a map defined on CobarMonomial objects
does this handle 0 dim vector spaces?
this is a huge timesink. try to do multiprocessing,
check methods for too much simplification
"""
dom = self.get_cplx()[i]
rng = self.get_cplx()[i + 1]
for bideg in dom._dict.keys():
out = []
dom_basis = dom._dict[bideg]
cols = len(dom_basis)
try:
rng_basis = rng._dict[bideg]
rows = len(rng_basis)
except KeyError:
rng._dict[bideg] = []
rows = 0
if cols == 0:
# we must account for this later!
cols = 1
#print "bideg in make maps",bideg
dom._maps[bideg] = ModMatrix.null(1, cols)
continue
if cols == 0:
cols = 1
if rows == 0:
rows = 1
#print "bideg in make maps. somethings 0", bideg
dom._maps[bideg] = ModMatrix.null(rows, cols)
continue
for mon in dom_basis:
value = mon._map_reduced()
vect = self.vector_from_element(value, i + 1, bideg[0],
bideg[1])
out.append(vect)
matrix = ModMatrix(out).get_transpose()
print " Made matrix: i, bideg, size", i, bideg, matrix.get_size()
dom._maps[bideg] = matrix
def rref_test(x, y, n):
for i in range(n):
xx = ModMatrix.random(x, y)
xx.compute_rref()
print xx, "\n"
print xx.rref, "\n"
print xx.basis_change, "\n"
pp = xx.basis_change
print pp * xx
rr = pp * xx
print rr == xx.rref
def rref_test(x,y,n):
for i in range(n):
xx = ModMatrix.random(x,y)
xx.compute_rref()
print xx, "\n"
print xx.rref, "\n"
print xx.basis_change, "\n"
pp = xx.basis_change
print pp * xx
rr = pp * xx
print rr == xx.rref
def solve_test(x,y,n):
for i in range(n):
AA = ModMatrix.random(x,y)
bb = ModVector.random(x)
print AA.can_solve(bb)
xx = AA.solve(bb)
print "A\n", AA, "\n"
print "rrefA\n", AA.get_rref(), "\n"
print "b\n", bb, "\n"
print "x\n", xx, "\n"
print "Ax\n", AA * xx
print AA * xx == ModMatrix([bb]).get_transpose()
def make_cohomology(self, filt, deg, wt):
"""
returns a cohomology object corr. to filt, deg, wt
#Returns 0 cohomology object if deg, wt doesn't appera
THIS MUTATES ._maps and ._dict IF NECESSARY!
"""
cplx = self.get_maps()
if filt == 0:
return "you know what this is!"
try:
#this checks to make sure cohom is non-zero here
B = cplx[filt]._maps[(deg, wt)]
B_basis = cplx[filt]._dict[(deg, wt)]
except KeyError:
if deg <= opts.bounds:
return Cohomology(ModMatrix.identity(1), \
ModMatrix.null(1,1))
else:
print filt, deg, wt
raise TypeError("We aren't computing that far!")
try:
#this checks to see if incoming map is 0 or not
A_basis = cplx[filt - 1]._dict[(deg, wt)]
A = cplx[filt - 1]._maps[(deg, wt)]
except KeyError:
A = ModMatrix.null(len(B_basis), 1)
A_basis = []
cplx[filt - 1]._maps[(deg, wt)] = A
cplx[filt - 1]._dict[(deg, wt)] = []
# We must now check dimensions of A_basis and B_basis
# to account for 0 diml vspaces
if len(B_basis) == 0:
#this means cohom is 0 diml
#resulting cohom object will not match up with vect/elt
#translation
A = ModMatrix.null(1,1)
B = ModMatrix.identity(1)
elif not B.row_count:
#print "B has no rows"
B = ModMatrix.null(1, len(B_basis))
cohom = Cohomology(B, A)
self.cohomology[filt][(deg,wt)] = cohom
def make_cohomology(self, filt, deg, wt):
"""
returns a cohomology object corr. to filt, deg, wt
#Returns 0 cohomology object if deg, wt doesn't appera
THIS MUTATES ._maps and ._dict IF NECESSARY!
"""
cplx = self.get_maps()
if filt == 0:
return "you know what this is!"
try:
#this checks to make sure cohom is non-zero here
B = cplx[filt]._maps[(deg, wt)]
B_basis = cplx[filt]._dict[(deg, wt)]
except KeyError:
if deg <= opts.bounds:
return Cohomology(ModMatrix.identity(1), \
ModMatrix.null(1,1))
else:
print filt, deg, wt
raise TypeError("We aren't computing that far!")
try:
#this checks to see if incoming map is 0 or not
A_basis = cplx[filt - 1]._dict[(deg, wt)]
A = cplx[filt - 1]._maps[(deg, wt)]
except KeyError:
A = ModMatrix.null(len(B_basis), 1)
A_basis = []
cplx[filt - 1]._maps[(deg, wt)] = A
cplx[filt - 1]._dict[(deg, wt)] = []
# We must now check dimensions of A_basis and B_basis
# to account for 0 diml vspaces
if len(B_basis) == 0:
#this means cohom is 0 diml
#resulting cohom object will not match up with vect/elt
#translation
A = ModMatrix.null(1, 1)
B = ModMatrix.identity(1)
elif not B.row_count:
#print "B has no rows"
B = ModMatrix.null(1, len(B_basis))
cohom = Cohomology(B, A)
self.cohomology[filt][(deg, wt)] = cohom
def matrix_mul(i,j,k,n):
for a in range(n):
xx = ModMatrix.random(i,j)
yy = ModMatrix.random(j,k)
print xx, "\n\n", yy, "\n\n", xx*yy, "\n"
def row_op_test(x,y,n):
for i in range(n):
xx = ModMatrix.random(x,y)
print xx
xx.el_row_op( random.randrange(opts.prime), 0, 1)
print xx
def rank_test(x, y, n):
for i in range(n):
AA = ModMatrix.random(x, y)
print "AA\n", AA, "\n"
print AA.get_rank()
def row_op_test(x, y, n):
for i in range(n):
xx = ModMatrix.random(x, y)
print xx
xx.el_row_op(random.randrange(opts.prime), 0, 1)
print xx
def matrix_mul(i, j, k, n):
for a in range(n):
xx = ModMatrix.random(i, j)
yy = ModMatrix.random(j, k)
print xx, "\n\n", yy, "\n\n", xx * yy, "\n"
def rank_test(x,y,n):
for i in range(n):
AA = ModMatrix.random(x,y)
print "AA\n", AA, "\n"
print AA.get_rank()
