def test_super():
ring = element.Q
U = Space(ring, 2, grade=0) # bosonic
V = Space(ring, 2, grade=1) # fermionic
lhs = (U @ U @ U).get_swap([0, 2, 1]).A
rhs = (U @ U @ V).get_swap([0, 2, 1]).A
assert eq(lhs, rhs)
lhs = (U @ V @ V).get_swap([0, 2, 1]).A
rhs = (U @ U @ U).get_swap([0, 2, 1]).A
assert eq(lhs, -rhs)
lhs = (V @ V @ V).get_swap([1, 2, 0]).A
rhs = (U @ U @ U).get_swap([1, 2, 0]).A
assert eq(lhs, rhs)
n = argv.get("n", 4)
part = argv.get("part", (2, ))
for a in range(n):
for b in range(n):
U = Space(ring, a, grade=0, name="U") # bosonic
V = Space(ring, b, grade=1, name="V") # fermionic
evn, odd = super_young(U, V, part)
print((evn, odd), end=" ", flush=True)
print()
def __ne__(self, other):
assert self.hom == other.hom
return not eq(self.A, other.A)
def __eq__(self, other):
assert self.hom == other.hom, "%s != %s" % (self.hom, other.hom)
return eq(self.A, other.A)
def weak_eq(self, other):
assert self.A.shape == other.A.shape
return eq(self.A, other.A)
def is_identity(self):
assert self.tgt == self.src, "wah?"
B = self.tgt.identity()
return eq(self.A, B.A)
def is_zero(self):
B = Lin.zero(self.tgt, self.src)
return eq(self.A, B.A)
def test():
p = argv.get("p", 2)
ring = element.FiniteField(p)
space = Space(ring)
zeros = space.zeros
rand = space.rand
dot = space.dot
kron = space.kron
direct_sum = space.direct_sum
identity = space.identity
coequalizer = space.coequalizer
compose = space.compose
rank = space.rank
pseudo_inverse = space.pseudo_inverse
tensor_swap = space.tensor_swap
sum_swap = space.sum_swap
schur = space.schur
is_zero = space.is_zero
is_identity = space.is_identity
s = tensor_swap(3, 4)
si = tensor_swap(4, 3)
#print(shortstr(s))
assert eq(dot(si, s), identity(3 * 4))
assert eq(dot(s, si), identity(4 * 3))
m, n = 2, 3
A1 = rand(m, n, 1, 1)
A2 = rand(m, n, 1, 1)
B = kron(A1, A2)
for m in range(1, 5):
I = identity(m * m)
s = tensor_swap(m, m)
f = coequalizer(I, s)
assert eq(compose(s, f), f)
assert rank(f) == [1, 3, 6, 10][m - 1]
# ---------------------------------
m = argv.get("m", 3)
n = argv.get("n", 4)
if argv.toric:
A = zeros(m, m)
for i in range(m):
A[i, i] = ring.one
A[i, (i + 1) % m] = -ring.one
elif argv.surface:
A = zeros(m - 1, m)
for i in range(m - 1):
A[i, i] = ring.one
A[i, (i + 1) % m] = -ring.one
else:
A = rand(m, n, p - 1, p - 1)
if argv.transpose:
A = A.transpose()
print("A:")
print(shortstr(A))
n, m = A.shape
In = identity(n)
Im = identity(m)
H1s = kron(Im, A), -kron(A, Im)
H1 = numpy.concatenate(H1s, axis=0) # horizontal concatenate
H0s = kron(A, In), kron(In, A)
H0 = numpy.concatenate(H0s, axis=1) # horizontal concatenate
assert is_zero(dot(H0, H1))
assert H1.shape == (n * m + m * n, m * m)
assert H0.shape == (n * n, n * m + m * n)
f0 = -tensor_swap(n, n)
a = direct_sum(-tensor_swap(m, n), -tensor_swap(n, m))
b = sum_swap(n * m, m * n)
assert is_identity(compose(b, b))
f1 = compose(a, b)
assert is_identity(compose(f1, f1))
f2 = tensor_swap(m, m)
assert eq(compose(f2, H1), compose(H1, f1))
lhs, rhs = ((compose(f1, H0), compose(H0, f0)))
#print("lhs:")
#print(shortstr(lhs))
#print("rhs:")
#print(shortstr(rhs))
assert eq(compose(f1, H0), compose(H0, f0))
g0 = coequalizer(f0, identity(f0.shape[0]))
assert eq(compose(H0, g0), compose(f1, H0, g0))
e = compose(H0, g0)
g1, J0 = coequalizer(f1, identity(f1.shape[0]), e)
assert eq(compose(H0, g0), compose(g1, J0))
e = compose(H1, g1)
g2, J1 = coequalizer(f2, identity(f2.shape[0]), e)
assert eq(compose(H1, g1), compose(g2, J1))
assert is_zero(compose(J1, J0))
n = J1.shape[0]
J1t = J1.transpose()
mz = rank(J1t)
mx = rank(J0)
print("J1t:", J1t.shape, rank(J1t))
print(shortstr(J1t))
print("J0:", J0.shape)
print(shortstr(J0))
print("n:", n)
print("mz:", mz)
print("mx:", mx)
print("k =", n - mx - mz)
def is_identity(self, A):
return eq(A, self.identity(A.shape[0]))
def is_zero(self, A):
return eq(A, self.zeros(*A.shape))