Algebra in Mathematica
- To: mathgroup at smc.vnet.net
- Subject: [mg56014] Algebra in Mathematica
- From: "jamievicary at NgOmSaPiAlM.com" <jamievicary at gmail.com>
- Date: Wed, 13 Apr 2005 01:11:01 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
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.