# Question:Problems with Physics package

## Question:Problems with Physics package

Maple

I just upgraded to Maple 12 because of its ability to perform abstract index calculations. However, I'm having trouble getting started with it. My first problem is with the Simplify command: if I define a completely symmetric tensor using the command

Define(T,symmetric);

and an antisymmetric tensor using the command

Define(w,antisymmetric);

then

Simplify(T[mu,nu,rho]*w[mu,nu]);

correctly returns 0. However, if I define T to be symmetric in only its first two indices,

Define(T[mu,nu,rho],symmetric={mu,nu});

then

Simplify(T[mu,nu,rho]*w[mu,nu]);

returns T[mu,nu,rho]*w[mu,nu]. Why doesn't Simplify recognize that the contraction yields zero?

My other problems are more general. How do I define a tensor with multiple types of indices? For example, I want to have spatial indices that run from 1 to 3 and spacetime indices that runs from 0 to 3.  I also want to have tetrad/frame indices and coordinate-basis indices. I thought I could use gaugeindices to accomplish that, but I can't figure out how to define an object with a gauge index.  Also, is there any way to convert an abstract tensor into an Array?

Thanks to anybody who can help.

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