[GiNaC-devel] Toggling index covariance in simplify_indexed()

[Richard B. Kreckel]

Hi Vladimir,

On 07/16/2016 12:00 PM, Vladimir V. Kisil wrote:
> 	I am confused by the following. The routine simplify_indexed() 
>   calls reposition_dummy_indices(), which has the freedom to toggle dummy
>   indices covariance to achieve canonical order. Leaving aside the
>   question "does the position of an index have geometrical/physical
>   significance and can be harmlessly toggled?", I come to the following
>   unpredictability of the GiNaC output in the different runs of the same
>   compiled programme:
> 
> #include <ginac/ginac.h>
> #include <fstream>
> using namespace std;
> using namespace GiNaC;
> 
> int main(){
> 	realsymbol x("x"), y("y");
> 	
> 	varidx mu(symbol("mu", "\\mu"), 2);
> 	ex e = clifford_unit(mu, diag_matrix(lst{-1,-1}));
> 
> 	ex V = lst_to_clifford(lst{x,y}, e);
> 
> 	cout << V << endl;
> 	// -> e~mu*[[x],[y]].mu
> 	cout << simplify_indexed(V) << endl;
> 	// in different runs can be either
> 	// (A) -> e~mu*[[x],[y]].mu (as above) or
> 	// (B) -> e.mu*[[x],[y]]~mu 
> 	cout << canonicalize_clifford(V*V) << endl;
> 	// depanding on the above outcomes:
> 	// (A) -> (e~mu*e~symbol6)*[[x],[y]].symbol6*[[x],[y]].mu
> 	// (B) -> -2*ONE*y^2-[[x],[y]]~symbol6*[[x],[y]]~mu*(e.symbol6*e.mu)-2*x^2*ONE
> 	cout << canonicalize_clifford(simplify_indexed(V)*simplify_indexed(V)) << endl;
> 	// (A) -> (e~mu*e~symbol10)*[[x],[y]].mu*[[x],[y]].symbol10
> 	// (B) -> -(e~symbol13*e~mu)*[[x],[y]].mu*[[x],[y]].symbol13-2*ONE*y^2-2*x^2*ONE
> 	cout << canonicalize_clifford(simplify_indexed(V)*V) << endl;
> 	// (A) -> -[[x],[y]]~symbol14*(e.symbol14*e~mu)*[[x],[y]].mu-2*ONE*y^2-2*x^2*ONE
> 	// (B) -> -2*ONE*y^2-[[x],[y]]~mu*[[x],[y]]~symbol20*(e.symbol20*e.mu)-2*x^2*ONE
> 	cout << canonicalize_clifford(expand_dummy_sum(simplify_indexed(V)*V)) << endl;
> 	// (A) -> -y^2*ONE-x^2*ONE
> 	// (B) -> y^2*(e.1*e~1)+x^2*(e.0*e~0)+x*y*(e.0*e~1)-x*y*(e~0*e.1)
> 
> 	return 0;
> }
> 
>   Any advice on usability/necessity of this behaviour?

IMHO, simplify_indexed() should try harder repositioning dummy indices,
so cases like yours always return the simplest form. Can you propose a
patch?

All my best,
   -richy.
-- 
Richard B. Kreckel
<http://in.terlu.de/~kreckel/>