@cindex @code{metric_tensor()}
@subsubsection General metric tensor
-The function @code{metric_tensor()} creates a general metric tensor with
-two indices that can be used to raise/lower tensor indices. The metric
-tensor is denoted as @samp{g} in the output and if its indices are of
+The function @code{metric_tensor()} creates a general symmetric metric
+tensor with two indices that can be used to raise/lower tensor indices. The
+metric tensor is denoted as @samp{g} in the output and if its indices are of
mixed variance it is automatically replaced by a delta tensor:
@example
@subsection Linear algebra
The @code{matrix} class can be used with indices to do some simple linear
-algebra (products of vectors and matrices, traces and scalar products):
+algebra (sums and products of vectors and matrices, traces and scalar
+products):
@example
@{
cout << e.simplify_indexed() << endl;
// -> [[ [[2*y+x]], [[4*y+3*x]] ]].i
- e = indexed(A, i, j) * indexed(X, i);
+ e = indexed(A, i, j) * indexed(X, i) + indexed(X, j);
cout << e.simplify_indexed() << endl;
- // -> [[ [[3*y+x,4*y+2*x]] ]].j
+ // -> [[ [[3*y+2*x,5*y+2*x]] ]].j
@}
@end example
-You can of course obtain the same results with the @code{matrix::mul()}
-and @code{matrix::trace()} methods but with indices you don't have to
-worry about transposing matrices.
+You can of course obtain the same results with the @code{matrix::add()},
+@code{matrix::mul()} and @code{matrix::trace()} methods but with indices you
+don't have to worry about transposing matrices.
Matrix indices always start at 0 and their dimension must match the number
of rows/columns of the matrix. Matrices with one row or one column are
vectors and can have one or two indices (it doesn't matter whether it's a
-row or a columnt vector). Other matrices must have two indices.
+row or a column vector). Other matrices must have two indices.
You should be careful when using indices with variance on matrices. GiNaC
doesn't look at the variance and doesn't know that @samp{F~mu~nu} and