def _delta_irr_rec(p, marking):
r"""
Internal recursive function called by :func:`delta_irr`.
"""
if len(p) == 0:
return 0
if marking[0] == 1:
m = marking[1]
a = marking[2]
i = p.index(m)
pp = Partition(p._list[:i] + p._list[i + 1:]) # the partition p'
N = (-1)**a * delta_std(pp._list + [m + 2], (1, m + 2, m - a))
for m1 in xrange(1, m - 1, 2):
m2 = m - m1 - 1
for a1 in xrange(max(0, a - m2), min(a, m1)):
a2 = a - a1 - 1
for p1, p2 in bidecompositions(pp):
l1 = sorted([m1] + p1._list, reverse=True)
l2 = sorted([m2 + 2] + p2._list, reverse=True)
N += (-1)**a2 * (_delta_irr_rec(Partition(l1),
(1, m1, a1)) *
spin_difference_for_standard_permutations(
Partition(l2), (1, m2 + 2, m2 - a2)))
return N
elif marking[0] == 2:
m1 = marking[1]
m2 = marking[2]
i1 = p.index(m1)
i2 = p.index(m2)
if m1 == m2: i2 += 1
if i2 < i1: i1, i2 = i2, i1
pp = Partition(p._list[:i1] + p._list[i1 + 1:i2] + p._list[i2 + 1:])
N = d(Partition(sorted(pp._list + [m1 + m2 + 1],
reverse=True))) / pp.centralizer_size()
# nb of standard permutations that corrresponds to extension of good
# guys
for p1, p2 in bidecompositions(Partition(pp)):
for k1 in xrange(1, m1, 2): # remove (k1|.) (k2 o m_2)
k2 = m1 - k1 - 1
q1 = Partition(sorted(p1._list + [k1], reverse=True))
q2 = Partition(sorted(p2._list + [k2 + m2 + 1], reverse=True))
for a in xrange(k1): # a is a angle
N += _delta_irr_rec(
q1, (1, k1, a)) * d(q2) / p2.centralizer_size()
for k1 in xrange(1, m2, 2): # remove (m_1 o k1) (k2|.)
k2 = m2 - k1 - 1
l1 = sorted(p1._list + [m1, k1], reverse=True)
l2 = sorted(p2._list + [k2 + 2], reverse=True)
for a in xrange(1, k2 + 1): # a is an angle for standard perm
N += (_delta_irr_rec(Partition(l1), (2, m1, k1)) *
spin_difference_for_standard_permutations(
Partition(l2), (1, k2 + 2, a)))
for m in pp.to_exp_dict(
): # remove (m_1 o k_1) (k_2 o m_2) for k1+k2+1 an other zero
q = pp._list[:]
del q[q.index(m)]
for p1, p2 in bidecompositions(Partition(q)):
for k1 in xrange(1, m, 2):
k2 = m - k1 - 1
q1 = Partition(sorted(p1._list + [m1, k1], reverse=True))
q2 = Partition(
sorted(p2._list + [k2 + m2 + 1], reverse=True))
N += _delta_irr_rec(
q1, (2, m1, k1)) * d(q2) / p2.centralizer_size()
return N
def _delta_irr_rec(p, marking):
r"""
Internal recursive function called by :func:`delta_irr`.
"""
if len(p) == 0:
return 0
if marking[0] == 1:
m = marking[1]
a = marking[2]
i = p.index(m)
pp = Partition(p._list[:i]+p._list[i+1:]) # the partition p'
N = (-1)**a* delta_std(
pp._list + [m+2],
(1,m+2,m-a))
for m1 in xrange(1,m-1,2):
m2 = m-m1-1
for a1 in xrange(max(0,a-m2),min(a,m1)):
a2 = a - a1 - 1
for p1,p2 in bidecompositions(pp):
l1 = sorted([m1]+p1._list,reverse=True)
l2 = sorted([m2+2]+p2._list,reverse=True)
N += (-1)**a2*(_delta_irr_rec(Partition(l1),(1,m1,a1)) *
spin_difference_for_standard_permutations(Partition(l2),(1,m2+2,m2-a2)))
return N
elif marking[0] == 2:
m1 = marking[1]
m2 = marking[2]
i1 = p.index(m1)
i2 = p.index(m2)
if m1 == m2: i2 += 1
if i2 < i1: i1,i2 = i2,i1
pp = Partition(p._list[:i1] + p._list[i1+1:i2] + p._list[i2+1:])
N = d(Partition(sorted(pp._list+[m1+m2+1],reverse=True))) / pp.centralizer_size()
# nb of standard permutations that corrresponds to extension of good
# guys
for p1,p2 in bidecompositions(Partition(pp)):
for k1 in xrange(1,m1,2): # remove (k1|.) (k2 o m_2)
k2 = m1-k1-1
q1 = Partition(sorted(p1._list+[k1],reverse=True))
q2 = Partition(sorted(p2._list+[k2+m2+1],reverse=True))
for a in xrange(k1): # a is a angle
N += _delta_irr_rec(q1, (1,k1,a)) * d(q2) / p2.centralizer_size()
for k1 in xrange(1,m2,2): # remove (m_1 o k1) (k2|.)
k2 = m2-k1-1
l1 = sorted(p1._list+[m1,k1],reverse=True)
l2 = sorted(p2._list+[k2+2],reverse=True)
for a in xrange(1,k2+1): # a is an angle for standard perm
N += (_delta_irr_rec(Partition(l1), (2,m1,k1)) *
spin_difference_for_standard_permutations(Partition(l2), (1,k2+2,a)))
for m in pp.to_exp_dict(): # remove (m_1 o k_1) (k_2 o m_2) for k1+k2+1 an other zero
q = pp._list[:]
del q[q.index(m)]
for p1,p2 in bidecompositions(Partition(q)):
for k1 in xrange(1,m,2):
k2 = m-k1-1
q1 = Partition(sorted(p1._list+[m1,k1],reverse=True))
q2 = Partition(sorted(p2._list+[k2+m2+1],reverse=True))
N += _delta_irr_rec(q1, (2,m1,k1)) * d(q2) / p2.centralizer_size()
return N
def _gamma_irr_rec(p, marking):
r"""
Internal recursive function called by :func:`gamma_irr`
"""
if len(p) == 0:
return 1
if marking[0] == 1:
m = marking[1]
a = marking[2]
i = p.index(m)
pp = Partition(p._list[:i] + p._list[i + 1:]) # the partition p'
N = gamma_std(pp._list + [m + 2], (1, m + 2, m - a))
for m1 in xrange(1, m - 1):
m2 = m - m1 - 1
for a1 in xrange(max(0, a - m2), min(a, m1)):
a2 = a - a1 - 1
for p1, p2 in bidecompositions(pp):
l1 = sorted([m1] + p1._list, reverse=True)
l2 = sorted([m2 + 2] + p2._list, reverse=True)
if (sum(l1) + len(l1)) % 2 == 0 and (sum(l2) +
len(l2)) % 2 == 0:
N -= (_gamma_irr_rec(Partition(l1), (1, m1, a1)) *
gamma_std(Partition(l2), (1, m2 + 2, m2 - a2)))
return N
elif marking[0] == 2:
m1 = marking[1]
m2 = marking[2]
i1 = p.index(m1)
i2 = p.index(m2)
if m1 == m2: i2 += 1
if i2 < i1: i1, i2 = i2, i1
pp = Partition(p._list[:i1] + p._list[i1 + 1:i2] + p._list[i2 + 1:])
N = gamma_std(pp._list + [m1 + 1, m2 + 1], (2, m1 + 1, m2 + 1))
for p1, p2 in bidecompositions(pp):
for k1 in xrange(1, m1): # remove (m'_1|.) (m''_1 o m_2)
k2 = m1 - k1 - 1
l1 = sorted(p1._list + [k1], reverse=True)
l2 = sorted(p2._list + [k2 + 1, m2 + 1], reverse=True)
if (sum(l1) + len(l1)) % 2 == 0 and (sum(l2) +
len(l2)) % 2 == 0:
for a in xrange(k1): # a is an angle
N -= (_gamma_irr_rec(Partition(l1), (1, k1, a)) *
gamma_std(Partition(l2), (2, k2 + 1, m2 + 1)))
for k1 in xrange(1, m2): # remove (m_1 o m'_2) (m''_2|.)
k2 = m2 - k1 - 1
l1 = sorted(p1._list + [m1, k1], reverse=True)
l2 = sorted(p2._list + [k2 + 2], reverse=True)
if (sum(l1) + len(l1)) % 2 == 0 and (sum(l2) +
len(l2)) % 2 == 0:
for a in xrange(1,
k2 + 1): # a is an angle for standard perm
N -= (_gamma_irr_rec(Partition(l1), (2, m1, k1)) *
gamma_std(Partition(l2), (1, k2 + 2, a)))
for m in pp.to_exp_dict(
): # remove (m_1, k_1) (k_2, m_2) for k1+k2+1 an other zero
q = pp._list[:]
del q[q.index(m)]
for p1, p2 in bidecompositions(Partition(q)):
for k1 in xrange(1, m):
k2 = m - k1 - 1
l1 = sorted(p1._list + [m1, k1], reverse=True)
l2 = sorted(p2._list + [k2 + 1, m2 + 1], reverse=True)
if (sum(l1) + len(l1)) % 2 == 0 and (sum(l2) +
len(l2)) % 2 == 0:
N -= (_gamma_irr_rec(Partition(l1), (2, m1, k1)) *
gamma_std(Partition(l2), (2, k2 + 1, m2 + 1)))
return N
else:
raise ValueError, "marking must be a 3-tuple of the form (1,m,a) or (2,m1,m2)"
def _gamma_irr_rec(p, marking):
r"""
Internal recursive function called by :func:`gamma_irr`
"""
if len(p) == 0:
return 1
if marking[0] == 1:
m = marking[1]
a = marking[2]
i = p.index(m)
pp = Partition(p._list[:i]+p._list[i+1:]) # the partition p'
N = gamma_std(pp._list + [m+2],(1,m+2,m-a))
for m1 in xrange(1,m-1):
m2 = m-m1-1
for a1 in xrange(max(0,a-m2),min(a,m1)):
a2 = a - a1 - 1
for p1,p2 in bidecompositions(pp):
l1 = sorted([m1]+p1._list,reverse=True)
l2 = sorted([m2+2]+p2._list,reverse=True)
if (sum(l1)+len(l1)) % 2 == 0 and (sum(l2)+len(l2)) % 2 == 0:
N -= (_gamma_irr_rec(Partition(l1), (1,m1,a1)) *
gamma_std(Partition(l2),(1,m2+2,m2-a2)))
return N
elif marking[0] == 2:
m1 = marking[1]
m2 = marking[2]
i1 = p.index(m1)
i2 = p.index(m2)
if m1 == m2: i2 += 1
if i2 < i1: i1,i2 = i2,i1
pp = Partition(p._list[:i1] + p._list[i1+1:i2] + p._list[i2+1:])
N = gamma_std(pp._list + [m1+1,m2+1],(2,m1+1,m2+1))
for p1,p2 in bidecompositions(pp):
for k1 in xrange(1,m1): # remove (m'_1|.) (m''_1 o m_2)
k2 = m1-k1-1
l1 = sorted(p1._list+[k1],reverse=True)
l2 = sorted(p2._list+[k2+1,m2+1],reverse=True)
if (sum(l1)+len(l1)) %2 == 0 and (sum(l2)+len(l2)) %2 == 0:
for a in xrange(k1): # a is an angle
N -= (_gamma_irr_rec(Partition(l1), (1,k1,a))*
gamma_std(Partition(l2),(2,k2+1,m2+1)))
for k1 in xrange(1,m2): # remove (m_1 o m'_2) (m''_2|.)
k2 = m2-k1-1
l1 = sorted(p1._list+[m1,k1],reverse=True)
l2 = sorted(p2._list+[k2+2],reverse=True)
if (sum(l1)+len(l1)) %2 == 0 and (sum(l2)+len(l2)) %2 == 0:
for a in xrange(1,k2+1): # a is an angle for standard perm
N -= (_gamma_irr_rec(Partition(l1), (2,m1,k1)) *
gamma_std(Partition(l2),(1,k2+2,a)))
for m in pp.to_exp_dict(): # remove (m_1, k_1) (k_2, m_2) for k1+k2+1 an other zero
q = pp._list[:]
del q[q.index(m)]
for p1,p2 in bidecompositions(Partition(q)):
for k1 in xrange(1,m):
k2 = m-k1-1
l1 = sorted(p1._list+[m1,k1],reverse=True)
l2 = sorted(p2._list+[k2+1,m2+1],reverse=True)
if (sum(l1)+len(l1))%2 == 0 and (sum(l2)+len(l2))%2 == 0:
N -= (_gamma_irr_rec(Partition(l1), (2,m1,k1)) *
gamma_std(Partition(l2),(2,k2+1,m2+1)))
return N
else:
raise ValueError, "marking must be a 3-tuple of the form (1,m,a) or (2,m1,m2)"
