[index] Algebra::PermutationGroup / Algebra::Permutation
This is the class of permutations. The elements are assumed to be the instances of Permutation.
::new(u, [g0, [g1, ...]])
::unit_group(d)
::unity(n)
::perm(a)
::symmetric(n)
::alternate(n)
::new(x)
::[[n0, [n1, [n2, ..., ]]]]
Returns the permutation [n0, n1, n2, ..., ]
.
Example:
a = Permutation[1, 2, 0] p a**2 #=> [2, 0, 1] p a**3 #=> [0, 1, 2]
::unity(d)
::cyclic2perm(c, n)
Returns the Permutation represented by c : the array of arrays of cyclic permutations, where n is the degree. This method is the inverse of decompose_cyclic.
Example:
Permutation.cyclic2perm([[1,6,5,4], [2,3]], 7) #=> [0, 6, 3, 2, 1, 4, 5] Permutation[0, 6, 3, 2, 1, 4, 5].decompose_cyclic #=> [[1,6,5,4], [2,3]]
unity
perm
degree
size
each
eql?(other)
==
hash
[i]
call
index(i)
right_act(other)
(g.right_act(h))[x] == h[g[x]]
.*
left_act(other)
(g.left_act(h))[x] == g[h[x]]
.inverse
inv
sign
conjugate(g)
g * self * g.inv
.decompose_cyclic
to_map
decompose_transposition