On Mon, Apr 25, 2005 at 07:04:29PM +0100, Vladimir Kisil wrote:
I added to your code just two lines at the end:
#include <iostream> #include <ginac/ginac.h> using namespace std; using namespace GiNaC;
int main(int argc, char** argv) { varidx i(symbol("i"), 2); varidx j(symbol("j"), 2);
matrix mink2_matr(2, 2, lst(-1, 0, 0, 1)); matrix a(1, 2, lst(symbol("a0"), symbol("a1")));
ex test1 = indexed(mink2_matr, i, i)*indexed(a, i); ex test2 = indexed(mink2_matr, j.toggle_variance(), i)*indexed(a, j);
cout << test1 << " = " << test1.simplify_indexed() << endl; cout << test2 << " = " << test2.simplify_indexed() << endl; cout << "test1 substituted = " << test1.simplify_indexed().subs(i == varidx(0, 2)) << endl; cout << "test2 substituted = " << test2.simplify_indexed().subs(i == varidx(0, 2)) << endl; return 0; }
and the output now becomes:
[[a0,a1]]~i*[[-1,0],[0,1]]~i~i = [[a0,a1]]~i*[[-1,0],[0,1]]~i~i [[a0,a1]]~j*[[-1,0],[0,1]].j~i = [[-a0,a1]]~i test1 substituted = -a0 test2 substituted = -a0
i.e., the initial difference between objects disappeared after the substitution was made. Should it be classified as a bug?
After substitution expression is not an indexed object any more, you get just particular element of a matrix (see ginac/matrix.cpp::eval_indexed) I think this is intended (but rather confusing) behaviour. Most indexed objects in GiNaC are tensors, while some are arrays (like indexed matrices). Expression indexed(m, i, j) means _different_ things for tensors and arrays. Unfortunately, mixing tensors and arrays (like some_matrix~i*some_vector.i) does NOT raise an exception (or compile-time error), thus, it is possible to write a lot of meaningless expressions :(
I would prefer if not all objects with indexes in GiNaC will be necessarily a tensors.
I would prefer if tensors and arrays would be completely different (have different types), so both tensor and array expressions are possible [and type-safe], but meaningless mixtures of both are not.
I had already a code which expand dummy-index summations in order to see "equality" (in non-tensor sense) similar to above, but I wish to check, that this cannot be already done by some standard tools.
You could use indexed matrices or write your own tensor (like tensdelta, tensepsilon and friends, see ginac/tensor.{cpp,h}). -- ROOT: an octopus made by nailing extra legs onto a cat.