From: Ronnie Brown <r.brown@bangor.ac.uk>
To: categories@mta.ca
Subject: Re: Maple program for cubical categories ?
Date: Thu, 15 Jul 1999 16:32:22 +0100 (BST) [thread overview]
Message-ID: <Pine.SOL.3.90.990715162605.2598F-100000@publix> (raw)
In-Reply-To: <199907150843.AA01264@irmast1.u-strasbg.fr>
This is a very sophisticated problem, involving rewrite theory.
Without the compositions, and with only one connection, there is work in
86. (with A.P.TONKS), ``Calculations with simplicial and cubical groups
in AXIOM'', {\em J. Symbolic Computation}, 17 (1994) 159-179.
But AXIOM is not the easiest to get working for you! I have not looked at
this for a long time.
The difficulties of using the interchange rule are quickly seen by
considering pre crossed and crossed modules. We actually did some
calculations of induced crossed modules in
92. (with C.D.WENSLEY), ``On finite induced crossed modules and the
homotopy 2-type of mapping cones'', {\em Theory
and Applications of Categories} 1(3) (1995) 54-71.
95. (with C.D.WENSLEY), ``Computing crossed modules induced by an
inclusion of a normal subgroup, with applications to
homotopy 2-types'', {\em Theory and Applications of Categories} 2 (1996)
3-16.
There is more on rewriting in Heyworth-Wensley
Mathematics, abstract
math.CO/9907082
Logged Rewriting Procedures with Application to Identities Among
Relations
I thoroughly appreciate the need!
Ronnie Brown
On Thu, 15 Jul 1999, Philippe Gaucher wrote:
> Bonjour,
>
> I have calculations to do in a cubical omega-category
> (see works of Brown, Higgins, etc... for the definition).
> I have to verify some equalities.
> I am wondering whether there is a program (Maple, anything else)
> in order to simplify automatically expressions containing
> only the usual operators like the three families of degeneracy
> maps of a cubical set with connections, operations +_j, and the
> usual face maps.
>
> Every composition of degeneracy maps and face maps can be
> ordered with the degeneracy maps of the cubical sets in the
> first place (in a canonical order), followed by the connection
> maps, followed by the face maps. But I do not see a canonical
> way to deal with +_j (because of the interchange law for example).
>
>
> pg.
>
Prof R. Brown, School of Mathematics,
University of Wales, Bangor
Dean St., Bangor, Gwynedd LL57 1UT, United Kingdom
Tel. direct:+44 1248 382474|office: 382475
fax: +44 1248 383663
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prev parent reply other threads:[~1999-07-15 15:32 UTC|newest]
Thread overview: 2+ messages / expand[flat|nested] mbox.gz Atom feed top
1999-07-15 8:43 Philippe Gaucher
1999-07-15 15:32 ` Ronnie Brown [this message]
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