[GiNaC-list] Don't do mix tensors and matrices (Was: How to convert epsilon_tensor in a matrix?)

[Marco André Ferreira Dias]

Hi Alexei,

thanks for your advice. I've changed my code, implementing all in the
scalar products, instead using matrices explicitly. But epsilon tensor
fully contracted with vectors still being a problem, since its isn't
transformable in the ordinary product of this vectors.
My problem is after compute a expression use it to do a Monte Carlo
integration of this values.
Regards,

Marco

On Sun, Feb 26, 2012 at 1:54 PM, Alexei Sheplyakov <
alexei.sheplyakov at gmail.com> wrote:

> Hello,
>
> On Sun, Feb 26, 2012 at 12:06:37PM -0300, Marco André Ferreira Dias wrote:
>
> > I have a very naive question: my program compute some dirac_traces, and
> > some epsilon_tensors arises in this process. I have to convert the
> > tensorial structure to matricial
>
> I don't think it's a good idea (see
> http://www.ginac.de/FAQ.html#matrix_indexed)
>
> > to compute it numerically
>
> And I don't think it's necessary for numeric computation.
>
> > but until now I don't figure out how to manipulate expressions like this
> > =============
> > [[31],[0.0],[0.0],[-31]]~sigma*[[6.3],[0.0],[0.0],[6.30]]~alpha*
> > [[19.33],[-1.108],[-5.4],[18.6]].gamma*eps.delta.sigma~gamma.alpha*
> > [[16.781197650788506337],[4.96],[11.38],[11.2]]~gamma
> > =============
>
> Don't convert tensor expressions to matrices, instead express them via
> invariant quantities, like this:
>
> #include <iostream>
> #include <ginac/ginac.h>
> using namespace std;
> using namespace GiNaC;
>
> int main()
> {
>        symbol q("q"), l("l"), m("m"), ldotq("ldotq"), D("D");
>        varidx mu(symbol("mu"), D), nu(symbol("nu"), D);
>
>        scalar_products sp;
>        sp.add(l, l, pow(l, 2));
>        sp.add(l, q, ldotq);
>
>        ex e = dirac_gamma(mu)*
>                (dirac_slash(l, D) + dirac_slash(q, D) + m*dirac_ONE())*
>                dirac_gamma(mu.toggle_variance())*
>                (dirac_slash(l, D) + m*dirac_ONE());
>        e = dirac_trace(e).simplify_indexed(sp);
>        e = e.collect(lst(l, ldotq, m));
>        cout << e << endl;
>        // -> (8-4*D)*l^2+(8-4*D)*ldotq+4*D*m^2
>        return 0;
> }
>
>
> See the fine manual (specifically, the paragraph 4.15.1.1, titled as
> `Dirac gamma matrices') for more details.
>
> Hope this helps,
>        Alexei
>
>
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