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 [BH82], Brown and Razak Salleh [BS99] and is surveyed in the first author's thesis [Hey99].

**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 [HW03] and [Hey99].

The current version is 2.34 for **GAP** 4.8, released on 20th October 2016.

The package may be obtained as a compressed tar file `idrel-2.34.tar.gz`

by ftp from one of the following sites:

any

**GAP**archive, e.g. http://www.gap-system.org/Packages/packages.html;the package GitHub repository: https://gap-packages.github.io/idrel.

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