Introduction This manual describes the &idrel; package for &GAP; 4.7 for computing the identities among relators of a group presentation using rewriting, logged rewriting, monoid polynomials, module polynomials and Y-sequences.

The theoretical background for these computations is contained in Brown and Huebschumann , Brown and Razak Salleh and is surveyed in the first author's thesis .

&idrel; is primarily designed for the computation of a minimal set of generators for the module of identities among relators. It also contains functions which compute logged rewrite systems for group presentations (and complete them where possible); functions for operations involving elements of monoid rings; and functions for operations with elements of right modules over monoid rings. The Y-sequences are used as a rewriting way of representing elements of a free crossed module (products of conjugates of group relators and inverse relators). The package is written entirely in &GAP;4, and requires no compilation.

The package is loaded into &GAP; with the LoadPackage command, and on-line help is available in the usual way.
gap> LoadPackage( "idrel" ); gap> ?idrel
A pdf version of the &idrel; manual is available in the doc directory of the home directory of &idrel;. The information parameter InfoIdRel has default value 0. When raised to a higher value, additional information is printed out. &idrel; was originally developed in 1999 using &GAP;3, partially supported by a University of Wales Research Assistantship for the first author, Anne Heyworth.

If you use &idrel; to solve a problem then please send a short email to the second author, to whom bug reports, suggestions and other comments should also be sent. You may reference the package by mentioning and .

The current version is &VERSION; of &LONGRELEASEDATE;.