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

[Vladimir V. Kisil]

	Dear All,

	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?

  Best wishes,
  Vladimir
-- 
Vladimir V. Kisil                 http://www.maths.leeds.ac.uk/~kisilv/
  Book:     Geometry of Mobius Transformations     http://goo.gl/EaG2Vu
  Software: Geometry of cycles          http://moebinv.sourceforge.net/