represent a permutation group
degree of the permutation group
set of generators for the permutation group
The function permgroup is used as a procedure and an unevaluated procedure call. As a procedure, permgroup checks its arguments and then either exits with an error or returns the unevaluated permgroup call.
The first argument is the degree of the group, and should be an integer. The second argument is a set of group generators. Each generator is represented in disjoint cycle notation. The generators may be named or unnamed. A named generator is an equation; the left operand is the generator's name, the right operand is the permutation in disjoint cycle notation.
A permutation in disjoint cycle notation is a list of lists. Each sub-list represents a cycle; the permutation is the product of these cycles. The cycle [a1,a2,...,an] represents the permutation which maps a1 to a2, a2 to a3, ..., an−1 to an, and an to a1. The identity element is represented by the empty list .
The permgroup function follows the convention that ``permutations act on the right''. In other words, if p1 and p2 are permutations, then the product of p1 and p2, p1 &* p2 is defined such that p1 &* p2⁡i=p2⁡p1⁡i for i=1..deg.
the following is not legal:
Error, (in permgroup) generators must represent products of disjoint cycles, but [[7, 2]] does not
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