An algebra with non-trivial relations is constructed as a quotient of an existing algebra, possibly a free algebra. For convenience, the necessary free algebra may be constructed in-line.

quo< F | relations > : AlgFP, Rel, .., Rel -> AlgFP

Given an fp-algebra F, and a set of relations relations over the generators of F, construct the quotient of F by the ideal of F defined by relations.

The expression defining F may be either simply the name of a previously constructed algebra, or an expression defining an fp-algebra.

If relations is a list then each term of the list is either a word, a relation, or a relation list.

A word is interpreted as a relator.

A relation consists of a pair of words, separated by `='. (See above).

A relation list consists of a list of words, where each pair of adjacent words is separated by `=': w_1 = w_2 = ... = w_r. This is interpreted as the relations w_1 = w_r, ..., w_(r - 1) = w_r.

Note that the relation list construct is only meaningful in the context of the fp-algebra constructor.

This function returns

• The quotient algebra A;
• The natural homomorphism phi : F -> A.

Given an ideal I of the algebra A, construct the quotient of A by the ideal I. The quotient is formed by taking the presentation for A and including the generating words of I as additional relations.