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Re: Algebra in Mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg56063] Re: Algebra in Mathematica
• From: "Steve Luttrell" <steve_usenet at _removemefirst_luttrell.org.uk>
• Date: Thu, 14 Apr 2005 08:56:16 -0400 (EDT)
• References: <d3ibcu$9qt$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

I responded to a similar question before, which you can find in the archives 
at

http://forums.wolfram.com/mathgroup/archive/2004/Jun/msg00363.html

Steve Luttrell

"jamievicary at NgOmSaPiAlM.com" <jamievicary at gmail.com> wrote in message 
news:d3ibcu$9qt$1 at smc.vnet.net...
> Dear all,
>
>    I am trying to implement an algebra in mathematica, but I don't
> want to use a matrix representation for it. So, I've got elements like
> A, B and C, and I want to tell Mathematica, for example, that A.B==-C,
> along with other identities. I then want to put some complicated
> expression in, like A.B.B.C.B-B.C.A+A.B.C.B.A and have Mathematica
> simplify it using the rules of the algebra. What's the best easiest way
> to implement this? The elements of my algebra form a group; are there
> group-theory capabilities in Mathematica that I can use to do what I
> want? What if I change my algebra so that it stops being a group (for
> example, make it nonassociative) --- would this then make things much
> harder?
>
>            Thanks very much!
>
>                Jamie.
>