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

[Vladimir V. Kisil]

	Dear Richard,
	
>>>>> On Fri, 12 Aug 2016 00:31:36 +0200, "Richard B. Kreckel" <kreckel at in.terlu.de> said:

    RK> 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?

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

    I can try, but this will not be fast.
-- 
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/