Hello!
Here is a useful class to handle permutations.
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class Perm:
def __init__(self, size, cycle=None):
self.size = size
self.data = range(size)
if cycle:
n = len(cycle)
for i in range(n):
self.data[cycle[i]] = cycle[(i+1) % n]
def __str__(self):
return str(self.data)
def __mul__(self, other):
if self.size != other.size:
print "error: different size"
return
tmp = Perm(self.size)
for key in range(tmp.size):
tmp.data[key] = self.data[other.data[key]]
return tmp
def __invert__(self): # ~p
tmp = Perm(self.size)
for i in range(tmp.size):
tmp.data[self.data[i]] = i
return tmp
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# Exemplary calculations
N = 4
E = Perm(N)
R1 = Perm(N,(0,1)) * Perm(N,(2,3))
R2 = Perm(N,(0,2)) * Perm(N,(1,3))
R3 = R1 * R2
# {E, R1, R2, R3} form D_2 group
H = Perm(N,(0,1,3,2))
print H, ~H, H*(~H)
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Regards,
Andrzej Kapanowski
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