Subsections

• Structure Constructors
• Element Constructors

Construct the free semigroup F on n generators, where n is a positive integer. The i-th generator may be referenced by the expression F.i, i = 1, ..., n. Note that a special form of the assignment statement is provided which enables the user to assign names to the generators of F. In this form of assignment, the list of generator names is enclosed within angle brackets and appended to the variable name on the left hand side of the assignment statement.

Construct the free monoid F on n generators, where n is a positive integer. The i-th generator may be referenced by the expression F.i, i = 1, ..., n. Note that a special form of the assignment statement is provided which enables the user to assign names to the generators of F. In this form of assignment, the list of generator names is enclosed within angle brackets and appended to the variable name on the left hand side of the assignment statement.

> F := FreeSemigroup(2);

The statement

> F<x, y> := FreeSemigroup(2);

Suppose S is an fp-semigroup for which generators have already been defined. A word is defined inductively as follows:

• A generator is a word;
• The product uv of the words u and v is a word;
• The power of a word, u^n, where u is a word and n is an integer, is a word.

Given a semigroup S defined on r generators and a sequence Q = [i_1, ..., i_s] of integers lying in the range [1, r], construct the word G.(i_1) G.(i_2) ... G.(i_s).

M ! 1 : MonFP -> MonFPElt

Construct the identity element (empty word) for the fp-monoid M.