def orbiplex(G, k=4):
#import numpy
#from gelim import zeros, dotx, rank, nullity
print("orbiplex: |G|=%d" % len(G))
items = G.items
k = argv.get("k", k)
for n in range(k):
write("|C_%d| ="%n)
#if n > len(items):
# break
tpls = list(uniqtuples(items, n))
perms = []
for perm in G:
_perm = {}
for key in tpls:
value = tuple(perm[i] for i in key)
_perm[key] = value
_perm = Perm(_perm, tpls)
perms.append(_perm)
G2 = Group(perms, tpls)
orbits = list(G2.orbits())
d = len(orbits)
write("%d,"%d)
def hecke(self):
bag0 = self.get_bag()
bag1 = self.get_bag()
points = [p for p in bag0 if p.desc == '0']
lines = [p for p in bag0 if p.desc == '1']
print(points)
print(lines)
flags = []
for p in points:
ls = [l for l in p.nbd if l != p]
print(p, ls)
for l in ls:
flags.append((p, l))
print("flags:", len(flags))
# for point in bag0:
# print point, repr(point.desc)
#items = [(point.idx, line.idx) for point in points for line in lines]
#items = [(a.idx, b.idx) for a in points for b in points]
items = [(a, b) for a in flags for b in flags]
# fixing two points gives the Klein four group, Z_2 x Z_2:
#for f in isomorph.search(bag0, bag1):
# if f[0]==0 and f[1]==1:
# print f
perms = []
for f in isomorph.search(bag0, bag1):
#print f
g = dict((bag0[idx], bag0[f[idx]]) for idx in list(f.keys()))
perm = {}
for a, b in items:
a1 = (g[a[0]], g[a[1]])
b1 = (g[b[0]], g[b[1]])
assert (a1, b1) in items
perm[a, b] = a1, b1
perm = Perm(perm, items)
perms.append(perm)
write('.')
print()
g = Group(perms, items)
print("group:", len(g))
orbits = g.orbits()
#print orbits
print("orbits:", len(orbits))
eq = numpy.allclose
dot = numpy.dot
n = len(flags)
basis = []
gen = []
I = identity2(n)
for orbit in orbits:
A = zeros2(n, n)
#print orbits
for a, b in orbit:
A[flags.index(a), flags.index(b)] = 1
print(shortstr(A))
print(A.sum())
#print
basis.append(A)
if A.sum() == 42:
gen.append(A)
assert len(gen) == 2
L = gen[0]
P = gen[1]
q = 2
assert eq(dot(L, L), L + q * I)
assert eq(dot(P, P), P + q * I)
assert eq(dot(L, dot(P, L)), dot(P, dot(L, P)))