On Tue, Sep 1, 2009 at 12:15 PM, Vladimir V. Kisil <kisilv@maths.leeds.ac.uk> wrote:

>>>>> On Tue, 25 Aug 2009 16:12:37 +0100, Chris Kelly <giltirn@gmail.com> said:

CK> grips with the clifford algebra classes. I am trying to perform
CK> the simple substitution:
CK> A_mu gamma_mu B_nu gamma_nu = A_mu A_nu delta_mu,nu (Euclidean space).

Why you are doing this replacement? I do not think it is mathematically
correct, it shall be:

A_mu gamma_mu B_nu gamma_nu + B_nu gamma_nu A_mu gamma_mu = A_mu A_nu delta_mu,nu

You can get that answer by canonicalize_clifford() method without any
substitution.

Indeed you are correct, it is only true when A=B. I over-generalised my example without thinking it through. In my main problem I only ever need to replace A_mu gamma_mu A_nu gamma_nu = A_mu A_nu delta_mu,nu. However my example still retains some validity in the sense that this replacement will not work either!

CK> Here is some example code:

CK> ex metric = unit_matrix(4); idx i(symbol("i"),4) ,
CK> j(symbol("j"),4); ex al_i = clifford_unit(i,metric); //Use
CK> // generalised clifford gamma matrices for euclidean space
CK> //Create generic 'slashed' symbols with euclidean metric

You may prefer to use delta tensor rather than unit matrices to
create this Clifford units---output of simplification will be more
transparent.

Thank you, i'll give this a try.

I don't suppose you have an answer to my question about whether there is some way to canonically order an expression by a set of rules rather than by the hash value such that i can find a pattern that is guaranteed to match?