ex ex::symmetrize(const lst & l);
ex ex::antisymmetrize(const lst & l);
ex ex::symmetrize_cyclic(const lst & l);
symmetrize an expression by returning the sum over all symmetric, antisymmetric or cyclic permutations of the specified list of objects, weighted by the number of permutations.
The three additional methods
ex ex::symmetrize();
ex ex::antisymmetrize();
ex ex::symmetrize_cyclic();
symmetrize or antisymmetrize an expression over its free indices.
Symmetrization is most useful with indexed expressions but can be used with
almost any kind of object (anything that is subs()able):
{
idx i(symbol("i"), 3), j(symbol("j"), 3), k(symbol("k"), 3);
symbol A("A"), B("B"), a("a"), b("b"), c("c");
cout << indexed(A, i, j).symmetrize() << endl;
// -> 1/2*A.j.i+1/2*A.i.j
cout << indexed(A, i, j, k).antisymmetrize(lst(i, j)) << endl;
// -> -1/2*A.j.i.k+1/2*A.i.j.k
cout << lst(a, b, c).symmetrize_cyclic(lst(a, b, c)) << endl;
// -> 1/3*{a,b,c}+1/3*{b,c,a}+1/3*{c,a,b}
}