[GiNaC-list] Equal indexed expressions

[Sheplyakov Alexei]

Hello,

On Mon, Apr 25, 2005 at 03:06:56PM +0100, Vladimir Kisil wrote:

> 		I am wondering how to convince GiNaC that the following to
>   expressions are equal:
> 
>   [[-1,0],[0,1]~mu~mu * a~mu        
>   [[-1,0],[0,1].nu~mu * a~nu      

First of all, I'm wondering how to convince _me_ that those expressions
are equal: the second expression is a vector, and the first one looks
like diagonal elements of a tensor of the 3'rd rank.

Second. Probably, you expected that

[[-1,0],[0,1]~mu~mu * a~mu is [-a~0, a~1]. 

[[-1, 0], [0, 1]].nu~mu * a~nu is [ -a~0, a~1]  too.

But that is NOT the case with GiNaC. In general: expression a.i a~i
has very little to do with a_0 a_0 - a_1 a_1 - ... - a_N a_N for a 
good reason (GiNaC is (was?) a library for calculation of Feynman
integrals, so dimension of indices are NOT required to be positive integers).

N.B.:
The `matrix' class CAN be used with indices to do some simple linear
algebra (probably, just to add more confusion). But this code

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

int main(int argc, char** argv)
{
	varidx i(symbol("i"), 2);
	varidx j(symbol("j"), 2);

	matrix mink2_matr(2, 2, lst(-1, 0, 0, 1));
	matrix a(1, 2, lst(symbol("a0"), symbol("a1")));

	ex test1 = indexed(mink2_matr, i, i)*indexed(a, i);
	ex test2 = indexed(mink2_matr, j.toggle_variance(), i)*indexed(a, j);

	cout << test1 << " = " << test1.simplify_indexed() << endl;
	cout << test2 << " = " << test2.simplify_indexed() << endl;
	return 0;
}

gives

[[a0,a1]]~i*[[-1,0],[0,1]]~i~i = [[a0,a1]]~i*[[-1,0],[0,1]]~i~i
[[a0,a1]]~j*[[-1,0],[0,1]].j~i = [[-a0,a1]]~i

(once again: first expression is a tensor 3'rd rank, while second expression
is a vector)
 
So, (unless I'm missing something fundamental) you are out of luck...


-- 
ROOT: an octopus made by nailing extra legs onto a cat.