After not finding the desired capabilities in base Mathematica, I am trying to use xAct`xTensor
package. It appears that I do not need most of it capabilities though: I have an expression with tensors, where indices go over $1,\dots,d$, $1,\dots,J$, or $1,\dots,S$, where positive integers $d,J,S$ are unknown, and need to expand simplify that expression given known properties of the tensors involved. I didn't find a dedicated way to specify a vector space in xAct`xTensor
, so I am assuming it is supposed to be a vBundle over 0-dimensional manifold. Thus, I am trying to define:
DefManifold[M0, 0, {}];
DefVBundle[vBd, M0, nd, {a, b, c, d, e, f, a1, b1, c1, d1, e1, f1}];
DefMetric[1, metricvBd[-a, -b], PrintAs -> "gd"];
Unfortunately, this fails with an error DefMetric::noicovd: Metrics in inner vbundles do not support covariant derivatives
. Why is that? Is there a way to specify that I do not need any derivatives (and, in fact, would be more than happy with the trivial metric $\delta_{ab}$) and avoid that error or a better library to use for that purpose?