Hi Vladimir,<br><br><div class="gmail_quote">On Tue, Sep 1, 2009 at 12:15 PM, Vladimir V. Kisil <span dir="ltr"><<a href="mailto:kisilv@maths.leeds.ac.uk">kisilv@maths.leeds.ac.uk</a>></span> wrote:<br><blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;">
<br>
>>>>> On Tue, 25 Aug 2009 16:12:37 +0100, Chris Kelly <<a href="mailto:giltirn@gmail.com">giltirn@gmail.com</a>> said:<br>
<br>
CK> grips with the clifford algebra classes. I am trying to perform<br>
CK> the simple substitution:<br>
CK> A_mu gamma_mu B_nu gamma_nu = A_mu A_nu delta_mu,nu (Euclidean space).<br>
<br>
Why you are doing this replacement? I do not think it is mathematically<br>
correct, it shall be:<br>
<br>
A_mu gamma_mu B_nu gamma_nu + B_nu gamma_nu A_mu gamma_mu = A_mu A_nu delta_mu,nu<br>
<br>
You can get that answer by canonicalize_clifford() method without any<br>
substitution.<br>
<br></blockquote><div> </div><div>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!<br>
</div><blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;">
CK> Here is some example code:<br>
<br>
CK> ex metric = unit_matrix(4); idx i(symbol("i"),4) ,<br>
CK> j(symbol("j"),4); ex al_i = clifford_unit(i,metric); //Use<br>
CK> // generalised clifford gamma matrices for euclidean space<br>
CK> //Create generic 'slashed' symbols with euclidean metric<br>
<br>
You may prefer to use delta tensor rather than unit matrices to<br>
create this Clifford units---output of simplification will be more<br>
transparent.<br>
<font color="#888888"><br></font></blockquote><div>Thank you, i'll give this a try.<br><br>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?</div></div><br>Best,<br>Chris<br>