Dear All, I recently noticed that GiNaC incorrectly expands products with dummy index summations, which is illustrated by the following program: #include <iostream> #include <ginac/ginac.h> using namespace std; using namespace GiNaC; #include <stdexcept> int main(){ realsymbol a("a"), b("b"), c("c"), d("d"); varidx mu(symbol("mu", "\\mu"), 2); try { ex e; e = (indexed(a, mu)*indexed(b, mu.toggle_variance())+1)*indexed(c, mu)*indexed(d, mu.toggle_variance()); cout << e.expand() << endl; // -> d.mu*c~mu*b.mu*a~mu+d.mu*c~mu e = pow(indexed(a, mu)*indexed(b, mu.toggle_variance())+1, 2); cout << e.expand() << endl; // -> 1+2*b.mu*a~mu+(b.mu)^2*(a~mu)^2 } catch (exception &p) { cerr << "Got problem: " << p.what() << endl; } } I made a patch to mul.cpp, ncmul.cpp, power.cpp which _partially_ fix this problem. The bigger test looks now like that: #include <iostream> #include <ginac/ginac.h> using namespace std; using namespace GiNaC; #include <stdexcept> int main(){ realsymbol a("a"), b("b"), c("c"), d("d"); varidx mu(symbol("mu", "\\mu"), 2), nu(symbol("nu", "\\nu"), 2); try { ex e; e = (indexed(a, mu)*indexed(b, mu.toggle_variance())+1)*indexed(c, mu)*indexed(d, mu.toggle_variance()); cout << e.expand() << endl << endl; // -> d.mu*c~mu*b.symbol6*a~symbol6+d.mu*c~mu e = indexed(c, mu)*indexed(d, mu.toggle_variance())*(indexed(a, mu)*indexed(b, mu.toggle_variance())+1); cout << e.expand() << endl << endl; // -> d.mu*c~mu+d.mu*a~symbol7*b.symbol7*c~mu e = (1+indexed(c, mu)*indexed(d, mu.toggle_variance()))*(indexed(a, mu)*indexed(b, mu.toggle_variance())+1); cout << e.expand() << endl << endl; // -> 1+b.mu*a~mu+b.mu*c~symbol8*a~mu*d.symbol8+d.mu*c~mu e = pow(2*indexed(a, mu)*indexed(b, mu.toggle_variance())+1, 2); cout << e.expand() << endl << endl; // -> 1+4*b.mu*a~mu*b.symbol9*a~symbol9+4*b.mu*a~mu e = pow(2*indexed(a, mu)*indexed(b, mu.toggle_variance())+1, 3); cout << e.expand() << endl << endl; // -> 1+6*b.mu*a~mu+12*b.mu*a~mu*a~symbol10*b.symbol10+8*b.symbol12*a~symbol12*b.mu*a~symbol11*b.symbol11*a~mu e = (indexed(a, mu, nu)*dirac_gamma(mu.toggle_variance()) * dirac_gamma(nu.toggle_variance()) + dirac_ONE()) * indexed(b, mu, nu)*dirac_gamma(mu.toggle_variance()) * dirac_gamma(nu.toggle_variance()); cout << e.expand() << endl << endl; // -> (gamma.mu*gamma.nu*gamma.mu*gamma.nu)*a~mu~nu*b~mu~nu+(gamma.mu*gamma.nu)*b~mu~nu e = (indexed(a, mu, nu)*dirac_gamma(mu.toggle_variance()) * dirac_gamma(nu.toggle_variance()) + dirac_ONE()) *( indexed(b, mu, nu)*dirac_gamma(mu.toggle_variance()) * dirac_gamma(nu.toggle_variance()) + dirac_ONE()); cout << e.expand() << endl << endl; // -> b~symbol16~symbol17*a~mu~nu*(gamma.mu*gamma.nu*gamma.symbol16*gamma.symbol17)+ONE+(gamma.mu*gamma.nu)*a~mu~nu+(gamma.mu*gamma.nu)*b~mu~nu e = (indexed(a, mu, nu)*dirac_gamma(mu.toggle_variance()) * dirac_gamma(nu.toggle_variance()) + dirac_ONE()) * indexed(b, mu.toggle_variance(), nu.toggle_variance())*dirac_gamma(mu) * dirac_gamma(nu); cout << e.expand() << endl << endl; // -> (gamma.mu*gamma.nu*gamma~mu*gamma~nu)*a~mu~nu*b.mu.nu+(gamma~mu*gamma~nu)*b.mu.nu e = pow(indexed(a, mu, nu)*dirac_gamma(mu.toggle_variance()) * dirac_gamma(nu.toggle_variance()), 2); cout << e.expand() << endl << endl; // -> (gamma.mu*gamma.nu*gamma.symbol18*gamma.symbol19)*a~mu~nu*a~symbol18~symbol19 e = pow(2*indexed(a, mu, nu)*dirac_gamma(mu.toggle_variance()) * dirac_gamma(nu.toggle_variance())+dirac_ONE(), 2); cout << e.expand() << endl << endl; // -> 4*(gamma.mu*gamma.nu*gamma.symbol18*gamma.symbol19)*a~mu~nu*a~symbol18~symbol19+ONE+4*(gamma.mu*gamma.nu)*a~mu~nu e = pow(2*indexed(a, mu, nu)*dirac_gamma(mu.toggle_variance()) * dirac_gamma(nu.toggle_variance())+dirac_ONE(), 3); cout << e.expand() << endl << endl; // -> ONE+8*a~symbol26~symbol27*a~mu~nu*a~symbol28~symbol29*(gamma.mu*gamma.nu*gamma.symbol26*gamma.symbol27*gamma.symbol28*gamma.symbol29)+6*(gamma.mu*gamma.nu)*a~mu~nu+4*(gamma.mu*gamma.nu*gamma.symbol24*gamma.symbol25)*a~mu~nu*a~symbol24~symbol25+4*a~symbol22~symbol23*a~mu~nu*(gamma.mu*gamma.nu*gamma.symbol22*gamma.symbol23)+4*a~symbol20~symbol21*a~mu~nu*(gamma.mu*gamma.nu*gamma.symbol20*gamma.symbol21) } catch (exception &p) { cerr << "Got problem: " << p.what() << endl; } } So the problem remains in the cases when one dummy index belongs to non-commutative part of product and other---to a commutative part. I do not know how to fix this situation in a simple way. I sent my patch as an attachment to a separate letter to this list (which will be likely hold till moderator's approval). It includes as well a slightly redesigned version of my previous patch for indexed.cpp and clifford.cpp (from the Thu Apr 28 18:17:55 CEST 2005). Best regards, Vladimir -- Vladimir V. Kisil email: kisilv@maths.leeds.ac.uk -- www: http://maths.leeds.ac.uk/~kisilv/