GAP (Kan) - Chapter 1: Introduction

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1 Introduction

### 1 Introduction

The Kan package started out as part of Anne Heyworth's thesis [Hey99], and was designed to compute induced actions of categories (see also [BH00]).

This version of Kan only provides functions for the computation of normal forms of representatives of double cosets of finitely presented groups, and is made available in support of the paper [BGHW06]. Existing methods for computing double cosets in GAP are described in [Lin91].

The package is loaded into GAP with the command

    gap> LoadPackage( "kan" );

The package may be obtained as a compressed tar file `kan-version.number.tar.gz` by ftp from one of the following sites:

- the Kan GitHub site: https://github.com/gap-packages.github.io/kan/.

- any GAP archive, e.g. https://www.gap-system.org/Packages/packages.html;

The package also has a GitHub repository at: https://github.com/gap-packages/kan/.

Some of the functions in the Automata package are used to compute word acceptors and regular expressions for the languages they accept.

The KBMag package is also used to compute a word acceptor of a group `G` when `G` has no finite rewriting system. If KBMag is not available (the user is not on a UNIX system, or the C-programs have not been compiled), the file `dckbmag.gi` will not be read, so methods for the functions detailed in section 2.4.1 will not be available.

Once the package is loaded, it is possible to check the installation is correct by running a test file of the manual examples with the following command. (The test file itself is `tst/fulltest.tst` or `tst/parttest.tst`, depending whether or not KBMag is available.)

    gap> ReadPackage( "kan", "tst/testall.g" );
    #I  Testing /Applications/gap/my-dev/pkg/kan/tst/fulltest.tst
    #I  No errors detected while testing package kan
    true

The information parameter `InfoKan` takes default value `0`. When raised to a higher value, additional information is printed out.

Once the package is loaded, the manual `doc/manual.pdf` can be found in the documentation folder. The `html` versions, with or without MathJax, may be rebuilt as follows.

    gap> InfoLevel( InfoKan );
    0
    gap> ReadPackage( "kan, "makedoc.g" );

Please send bug reports, suggestions and other comments to the second author, or use the GitHub issue tracker at https://github.com/gap-packages/kan/issues/new.

Additional information can be found on the Computational Higher-dimensional Discrete Algebra website at http://pages.bangor.ac.uk/~mas023/chda/.

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