def test_young0():
ring = element.Q
n = argv.get("n", 3)
part = argv.get("part", (1, 1, 1))
assert sum(part) == n
V = Space(ring, n)
# build action of symmetric group on the space V
items = list(range(n))
gen1 = []
gen2 = []
for i in range(n - 1):
perm = dict((item, item) for item in items)
perm[items[i]] = items[i + 1]
perm[items[i + 1]] = items[i]
g = Perm(perm, items)
gen1.append(g)
A = elim.zeros(ring, n, n)
for k, v in perm.items():
A[v, k] = ring.one
lin = Lin(V, V, A)
gen2.append(lin)
perms = mulclose(gen1)
G = Group(perms, items)
#print(G)
action = mulclose_hom(gen1, gen2)
for g in G:
for h in G:
assert action[g *
h] == action[g] * action[h] # check it's a group hom
young = Young(G, part)
rowG = young.get_rowperms()
print("rowG", len(rowG))
colG = young.get_colperms()
print("colG", len(colG))
horiz = None
for g in rowG:
P = action[g]
horiz = P if horiz is None else (horiz + P)
vert = None
for g in colG:
P = action[g]
s = g.sign()
P = ring.promote(s) * P
vert = P if vert is None else (vert + P)
A = horiz * vert
assert vert * vert == len(colG) * vert
assert horiz * horiz == len(rowG) * horiz
print("part:", part)
print(young)
print("rank:", A.rank())
print("is_zero:", A.is_zero())
print(A)
#if not A.is_zero():
# print(A)
print()
def test_young():
# code ripped from qu.py
d = argv.get("d", 2)
n = argv.get("n", 3)
p = argv.get("p")
if p is None:
ring = element.Q
else:
ring = element.FiniteField(p)
print("ring:", ring)
space = Space(ring, d)
# tensor power of the space
tspace = reduce(matmul, [space] * n)
# build action of symmetric group on the tensor power
items = list(range(n))
gen1 = []
gen2 = []
for i in range(n - 1):
perm = dict((item, item) for item in items)
perm[items[i]] = items[i + 1]
perm[items[i + 1]] = items[i]
g = Perm(perm, items)
gen1.append(g)
lin = tspace.get_swap([g[i] for i in items])
#print(lin.hom)
gen2.append(lin)
perms = mulclose(gen1)
G = Group(perms, items)
#print(G)
action = mulclose_hom(gen1, gen2)
for g in G:
for h in G:
assert action[g *
h] == action[g] * action[h] # check it's a group hom
# Build the young symmetrizers
projs = []
part = argv.get("part")
parts = list(partitions(n)) if part is None else [part]
for part in parts:
assert sum(part) == n
t = Young(G, part)
rowG = t.get_rowperms()
colG = t.get_colperms()
horiz = None
for g in rowG:
P = action[g]
horiz = P if horiz is None else (horiz + P)
vert = None
for g in colG:
P = action[g]
s = g.sign()
P = ring.promote(s) * P
vert = P if vert is None else (vert + P)
A = horiz * vert
assert vert * vert == len(colG) * vert
assert horiz * horiz == len(rowG) * horiz
#A = A.transpose()
projs.append(A)
print("part:", part)
print(t)
print("rank:", A.rank())
print("is_zero:", A.is_zero())
#if not A.is_zero():
# print(A)
print()