39.1 Comparison of Permutations

Two permutations are equal if they move the same points and all these points have the same images under both permutations.

The permutation p₁ is smaller than p₂ if p₁ ¹ p₂ and i^p₁ < i^p₂ where i is the smallest point with i^p₁ ¹ i^p₂. Therefore the identity permutation is the smallest permutation. (see also Comparison Operations for Elements)

Permutations can be compared with certain other GAP objects, see Comparisons for the details.

gap> (1,2,3) = (2,3,1);
true
gap> (1,2,3) * (2,3,4) = (1,3)(2,4);
true
gap> (1,2,3) < (1,3,2);      # 1^(1,2,3) = 2 < 3 = 1^(1,3,2)
true
gap> (1,3,2,4) < (1,3,4,2);  # 2^(1,3,2,4) = 4 > 1 = 2^(1,3,4,2)
false

is the smallest permutation that generates the same cyclic group as the permutation perm. This is very efficient, even when perm has large order.

gap> SmallestGeneratorPerm( (1,4,3,2) );
(1,2,3,4)

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