20.2 Operations for Permutations

p1 * p2

The operator * evaluates to the product of the two permutations p1 and p2.

p1 / p2

The operator / evaluates to the quotient p1 * p2^{-1} of the two permutations p1 and p2.

LeftQuotient( p1, p2 )

LeftQuotient returns the left quotient p1^{-1} * p2 of the two permutations p1 and p2. (This can also be written p1 mod p2.)

p ^ i

The operator ^ evaluates to the i-th power of the permutation p.

p1 ^ p2

The operator ^ evaluates to the conjugate p2^{-1} * p1 * p2 of the permutation p1 by the permutation p2.

Comm( p1, p2 )

Comm returns the commutator p1^{-1} * p2^{-1} * p1 * p2 of the two permutations p1 and p2.

i ^ p

The operator ^ evaluates to the image i^p of the positive integer i under the permutation p.

i / p

The operator / evaluates to the preimage i^{p^{-1}} of the integer i under the permutation p.

list * p
p * list

The operator * evaluates to the list of products of the permutations in list with the permutation p. That means that the value is a new list new such that new[i] = list[i] * p respectively new[i] = p * list[i].

list / p

The operator / evaluates to the list of quotients of the permutations in list with the permutation p. That means that the value is a new list new such that new[i] = list[i] / p.

For the precedence of the operators see Operations.

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