Given words u and v, and a generator x, belonging to a semigroup S, return the word obtained from u by replacing each occurrence of x by v.

Suppose u and v are words belonging to the same semigroup S, and that f is an integer such that 1 <= f <= # u. If v is a subword of u, the function returns true, as well as the least integer l such that:

• l >= f; and,
• v appears as a subword of u, starting at the l-th letter of u.

If no such l is found, Match returns only false.

A random word of length l in the generators of the semigroup S, where m <= l <= n.

The word obtained by cyclically permuting the word u by n places. If n is positive, the rotation is from left to right, while if n is negative the rotation is from right to left. In the case where n is zero, the function returns u.

Given words u and v belonging to a semigroup S, and non-negative integers f and n, this function replaces the substring of u of length n, starting at position f, by the word v. Thus, if u = x_(i_1) ... x_(i_f) ... x_(i_(f + n - 1)) ... x_(i_m) then the substring x_(i_f) ... x_(i_(f + n - 1)) is replaced by v. If u and v belong to a monoid M and the function is invoked with v = Id(M), then the substring x_(i_f) ... x_(i_(f + n - 1)) of u is deleted.

The subword of the word u comprising the n consecutive letters commencing at the f-th letter of u.

Eltseq(u) : SgpFPElt -> [ SgpFPElt ]

The sequence obtained by decomposing u into the indices of its constituent generators. Thus, if u = x_(i_1) ... x_(i_m), then the sequence constructed by ElementToSequence is [i_1, i_2, ..., i_m].