# String Operations on Words

## `Eliminate(u, x, v): SgpFPElt, SgpFPElt, SgpFPElt -> SgpFPElt`

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 $v$.

## `Match(u, v, f): SgpFPElt, SgpFPElt, RngIntElt -> BoolElt, RngIntElt`

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

**(a)**
$l\geq f$; and,

**(b)**
$v$ appears as a subword of $u$, starting at the $l$-th letter of $u$.

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

## `Random(S, m, n): SgpFP, RngIntElt, RngIntElt -> SgpFPElt`

A random word of length $l$ in the generators of the semigroup $S$, where $m \leq l \leq n$.

## `RotateWord(u, n): SgpFPElt, RngIntElt -> SgpFPElt`

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 $u$.

## `Substitute(u, f, n, v): SgpFPElt, RngIntElt, SgpFPElt, RngIntElt -> SgpFPElt`

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 $u = x_{i_1}\cdots x_{i_f}\cdots x_{i_{f+n-1}}\cdots x_{i_m}$ then the substring $x_{i_f}\cdots x_{i_{f+n-1}}$ 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 $x_{i_f}\cdots x_{i_{f+n-1}}$ of $u$ is deleted.

## `Subword(u, f, n): SgpFPElt, RngIntElt, RngIntElt -> SgpFPElt`

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

## `ElementToSequence(u): SgpFPElt -> [ SgpFPElt ]`

## `Eltseq(u): SgpFPElt -> [ SgpFPElt ]`

The sequence obtained by decomposing $u$ into the indices of its constituent generators. Thus, if $u = x_{i_1}\ldots x_{i_m}$, then the sequence constructed by `ElementToSequence` is $[i_1,i_2, \ldots, i_m]$.