[GiNaC-list] Question (Generic Clifford Algebra)

[Javier Ros Ganuza]

Following Vladimir's  :)  instructions...

I implemented it, but I've found a problem with the output, probably due
to my lack of knowledge :(.

For reference the listing is 

---
//c++ clifford.cc -o clifford -lcln -lginac

#include <iostream>
using namespace std;

#include <ginac/ginac.h>
using namespace GiNaC;

int main()
{

varidx nu(symbol("nu", "\\nu"), 3), mu(symbol("mu", "\\mu"), 3), xi
(symbol("xi", "\\xi"), 3),  rho(symbol("rho", "\\rho"),3);

ex basis1 = clifford_unit(mu, diag_matrix(lst(1, 1, 1)));
ex basis2 = clifford_unit(nu, diag_matrix(lst(1, 1, 1)));

symbol a1("a1"),a2("a2"),b1("b1"),b2("b2"),c1("c1"),c2("c2");

ex vector1 = lst_to_clifford(lst(a1,b1,c1), rho, basis1);
ex vector2 = lst_to_clifford(lst(a2,b2,c2), rho, basis1);

cout << 2*vector1+vector2 << endl;

cout << 2*vector1*vector2 << endl;

cout << lst_to_clifford(lst(1, 0, 0), rho, basis1) + lst_to_clifford(lst
(0, 1, 0), rho, basis1) << endl;

return 0;
}

---

And the output

$ ./clifford
2*[[a1],[b1],[c1]].rho*e~rho+e~rho*[[a2],[b2],[c2]].rho
2*[[a1],[b1],[c1]].rho*ONE*[[a2],[b2],[c2]].rho*e~rho~rho
[[0],[1],[0]].rho*e~rho+e~rho*[[1],[0],[0]].rho


As it can be see the elements, [[a1],[b1],[c1]].rho, seem indivisible.
There are not trivial groupings being made, like,

[[0],[1],[0]].rho*e~rho+e~rho*[[1],[0],[0]].rho -> [[1],[1],
[0]].rho*e~rho

I tried to simplify_indexed but the result keeps the same.

Also at the tutorial, when dealing with generic clifford algebras,
refered Ginac output for elements of a Clifford Algebra are reflected as

v~0 e.0 + v~1 e.1 + ... + v~n e.n

so exhibiting that they are some how divisible.

Also covariant and contravariant indexes are interchanged in comparison
with the tutorial.


Any clues???.

Thanks for your help

Javier Ros