def permutation_vector(g):
"""
The distance matrix obtained by permuting taxa according
to the permutation g \in SymmetricGroup(n).
"""
n = g.parent().degree()
M = distance_matrix(n)
M = permutation_action(g,permutation_action(g,M).transpose()).transpose()
perm_vec = list(np.array(M)[triu_indices(n, 1)])
return perm_vec
def interesting_permutations(S):
m,n = (S.nrows(), S.ncols())
Sr = SymmetricGroup(m)
Sc = SymmetricGroup(n)
try:
( (g,h) for g in Sr for h in Sc
if g != Sr.identity() and h != Sc.identity() and
S == permutation_action(h, permutation_action(g, S).transpose()).transpose() ).next()
except StopIteration:
return 0
return 1
def orbit(S):
m,n = (S.nrows(), S.ncols())
Sr = SymmetricGroup(m)
Sc = SymmetricGroup(n)
ret = []
mats = [
permutation_action(h, permutation_action(g, S).transpose()).transpose()
for g in Sr for h in Sc
]
for M in mats:
if M not in ret:
ret.append(M)
return ret
def ray_magic(C,n):
ray_sets = [Set([ray_sign_vector(symmetric_matrix(n,r)) for r in cone]) for cone in C]
canonical = ray_sets[0]
d = {}
for g in SymmetricGroup(n):
permute = Set([tuple(permutation_action(g, v)) for v in canonical])
d[permute] = d.get(permute, []) + [g]
return d
def cusp_sums_from_signature_to_standard_basis(cuspsums,signatures,level):
"""
Converts a list of cuspsums where each entry is a list of multiplicities with respect
to the input signature order. To a list of cuspsums where each entry is a list of multiplicities
with respect to the standard order of the cusps.
"""
P = Permutation([cusp_number_from_signature(s,level)+1 for s in signatures]).inverse()
return [permutation_action(P,s) for s in cuspsums]
def test_permutation(g,R):
Rp = permute_matrix(g,R)
pat = map(ray_sign_pattern, [R,Rp])
vec = np.array(permutation_action(g, ray_sign_vector(R)))
if vec[0]==-1:
vec *= -1
pred = vector(list(vec))
d = {-1:"-", 1:"+"}
pred = "".join(map(d.get, pred))
#print R,"\n\n",Rp
#print "p0: %s\tp': %s\tp_pred: %s" % (pat[0], pat[1], pred)
assert pred==pat[1]
def permute_matrix(g, M):
mat = permutation_action(g, permutation_action(g, M).transpose()).transpose()
mat.set_immutable()
return mat
def row_orbit(M):
mats = [permutation_action(g, M) for g in SymmetricGroup(M.nrows())]
[m.set_immutable() for m in mats]
return mats
def col_permutation_action(g, M):
M = permutation_action(g, M.transpose()).transpose()
M.set_immutable()
return M