AddRelation(S, r, i) : SgpFP, Rel, RngIntElt -> SgpFP

Given an fp-semigroup S and a relation r in the generators of S, create the quotient semigroup obtained by adding the relation r to the defining relations of S. If an integer i is specified as third argument, insert the new relation after the i-th relation of S. If the third argument is omitted, r is added to the end of the relations that are carried across from S.

Given an fp-semigroup S and a relation r that occurs among the given defining relations for S, create the semigroup T, having the same generating set as S but with the relation r removed.

DeleteRelation(S, i) : SgpFP, RngIntElt -> SgpFP

Given an fp-semigroup S and an integer i, 1 <= i <= m, where m is the number of defining relations for S, create the semigroup T having the same generating set as S but with the i-th relation omitted.

Given an fp-semigroup S and relations r_1 and r_2 in the generators of S, where r_1 is one of the given defining relations for S, create the semigroup T having the same generating set as S but with the relation r_1 replaced by the relation r_2.

ReplaceRelation(S, i, r) : SgpFP RngIntElt, Rel -> SgpFP

Given an fp-semigroup S, an integer i, 1 <= i <= m, where m is the number of defining relations for S, and a relation r in the generators of S, create the semigroup T having the same generating set as S but with the i-th relation of S replaced by the relation r.

Given an fp-semigroup S with presentation < X | R >, create the semigroup T with presentation < X union { y } | R >, where y denotes a new generator.

AddGenerator(S, w) : SgpFP, SgpFPElt -> SgpFP

Given an fp-semigroup S with presentation < X | R > and a word w in the generators of S, create the semigroup T with presentation < X union { y } | R union { y = w } >, where y denotes a new generator.

Given an fp-semigroup S with presentation < X | R > and a generator y of S such that either S has no relations involving y, or a single relation r containing a single occurrence of y, create the semigroup T with presentation < X - { y } | R - { r } >.