Dear all, I am new to GiNaC and am currently trying to get to grips with the clifford algebra classes. I am trying to perform the simple substitution: A_mu gamma_mu B_nu gamma_nu = A_mu A_nu delta_mu,nu (Euclidean space). The problem i am having is that the pattern match is not consistent over repeated use of the executable: sometimes the pattern will match, at other times it will not. It looks to me that this is related to the ordering of the expressions. Here is some example code: ----------------------------------------------------------------------------------------------------------------------------------- #include<iostream> #include<vector> #include<sstream> #include<ginac/ginac.h> using namespace std; using namespace GiNaC; //Aim is to identify A_mu gamma_mu B_nu gamma_nu == A_mu B_nu delta_mu,nu int main(){ ex metric = unit_matrix(4); idx i(symbol("i"),4) , j(symbol("j"),4); ex al_i = clifford_unit(i,metric); //Use generalised clifford gamma matrices for euclidean space ex al_j = clifford_unit(j,metric); //Create generic 'slashed' symbols with euclidean metric ex s1 = indexed(symbol("A"),i)*al_i; ex s2 = indexed(symbol("B"),j)*al_j; //Form the product ex prod = s1*s2; cout << s1*s2 << endl; //Attempt to match to patterns idx w1(wild(1),4), w2(wild(2),4); indexed in2_w1 = indexed(wild(2),w1); indexed in3_w2 = indexed(wild(3),w2); ex al_w1 = clifford_unit(w1,metric); ex al_w2 = clifford_unit(w2,metric); ex spat2_w1 = in2_w1*al_w1; ex spat3_w2 = in3_w2*al_w2; ex mpat = spat2_w1 * spat3_w2; cout << "MATCHING TO PATTERN: " << mpat << endl; cout << prod.match(mpat) << endl; ex mpat2 = in2_w1 * in3_w2 * al_w1 * al_w2; cout << "MATCHING TO PATTERN: " << mpat2 << endl; cout << prod.match(mpat2) << endl; ex mpat3 = in3_w2 * in2_w1 * al_w1 * al_w2; cout << "MATCHING TO PATTERN: " << mpat3 << endl; cout << prod.match(mpat3) << endl; return 0; } ----------------------------------------------------------- The output of this example is as follows: B.j*(e.i*e.j)*A.i <----- matching this against pattern MATCHING TO PATTERN: (e.($1)*e.($2))*$3.($2)*$2.($1) 0 MATCHING TO PATTERN: (e.($1)*e.($2))*$3.($2)*$2.($1) 0 MATCHING TO PATTERN: (e.($1)*e.($2))*$3.($2)*$2.($1) 0 So the expressions seem to all be reordered consistently, but in a different ordering to the object to which we wish to match. If i then add more code, reproducing the above code for the first pattern but using different wildcard indices: ----------------------------------------------------------- //Create new indices, perhaps hash ordering will be correct for these? idx w4(wild(4),4), w5(wild(5),4); indexed in2_w4 = indexed(wild(2),w4); indexed in3_w5 = indexed(wild(3),w5); ex al_w4 = clifford_unit(w4,metric); ex al_w5 = clifford_unit(w5,metric); ex spat2_w4 = in2_w4*al_w4; ex spat3_w5 = in3_w5*al_w5; ex mpat4 = spat2_w4 * spat3_w5; cout << "MATCHING TO PATTERN: " << mpat4 << endl; cout << prod.match(mpat4) << endl; ---------------------------------------------------------- The output sometimes (but not always) matches: First run: (object to match output as B.j*(e.i*e.j)*A.i ) MATCHING TO PATTERN: $2.($4)*(e.($4)*e.($5))*$3.($5) 0 Second run: (object to match output as (e.i*e.j)*B.j*A.i ) MATCHING TO PATTERN: (e.($4)*e.($5))*$3.($5)*$2.($4) 1 Third run: (object to match output as B.j*(e.i*e.j)*A.i ) <---- notice this is the same as the first run MATCHING TO PATTERN: (e.($4)*e.($5))*$3.($5)*$2.($4) 1 So for some reason the pattern matching is ordering dependent in a way that cannot be controlled. Strangely even if the pattern matches for a given run, the substitution code ------------------------------------------------- //Pattern sometimes matches, try a substitution for identity ex ident = in2_w4 * in3_w5 * delta_tensor(w4,w5); cout << "SUBSTITUTION RESULT:" << prod.subs(mpat4==ident) << endl; cout << "SUBSTITUTION RESULT (ALGEBRAIC):" << prod.subs(mpat4==ident,subs_options::algebraic) << endl; -------------------------------------------------- always seems to fail (or is ignored?) Second run: (object to match output as (e.i*e.j)*B.j*A.i ) SUBSTITUTION RESULT:(e.i*e.j)*B.j*A.i SUBSTITUTION RESULT (ALGEBRAIC):(e.i*e.j)*B.j*A.i Third run: (object to match output as B.j*(e.i*e.j)*A.i ) SUBSTITUTION RESULT:B.j*(e.i*e.j)*A.i SUBSTITUTION RESULT (ALGEBRAIC):B.j*(e.i*e.j)*A.i Does anyone know how to solve these issues? Thanks, Chris K