Elementary Tietze Transformations

AddRelation(S, r) : SgpFP, Rel -> SgpFP
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.
DeleteRelation(S, r) : SgpFP, Rel -> SgpFP
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.
ReplaceRelation(S, r1, r2) : SgpFP, Rel, Rel -> SgpFP
Given an fp-semigroup S and relations r1 and r2 in the generators of S, where r1 is one of the given defining relations for S, create the semigroup T having the same generating set as S but with the relation r1 replaced by the relation r2.
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.
AddGenerator(S) : SgpFP -> SgpFP
Given an fp-semigroup S with presentation < X | R >, create the semigroup T with presentation < X ∪{ 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 ∪{ y } | R ∪{ y = w } >, where y denotes a new generator.
DeleteGenerator(S, y) : SgpFP, SgpFPElt -> SgpFP
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 } >.
V2.28, 13 July 2023