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MathGroup Archive 2005

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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.


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