:

## Maple 11, Tensors in Physics Package: Possible Bugs or Limitations

Maple
Here are some possible bugs or limitations that I have come across while working with Tensors in the new physics package. I have done best of my efforts looking into the documentation, but it is still possible that the bugs I am listing are not bugs at all but outcome of lack of my knowledge in using Maple. My intention of creating this blog is to not to criticize but to help the Physics package development team in making updates. I appreciate their efforts for developing a much needed package for areas like fluid mechanics, continuum mechanics, theory relativity etc. Platform I am using: Maple Ver 11.01 on Mac OS X 10.4.10 Following is my setup environment. Setup(coordinatesystems = {X, Y}, spacetimeindices=lowercaselatin,dimension = 3, differentiationvariables=X, signature = `+`); Possible Bugs/Limitations: 1) If T is a symmetric tensor and w is an antisymmetric tensor, then it is well known that product of T and w is zero. Define(T, symmetric): Define(w, antisymmetric): eq:=T[i,j]*w[i,j]; Simplify(eq) command prints zero, which is correct. But if, eq:=T[i,j](X)*w[i,j](X); Now, the Simplify command cannot conclude that the product is zero. It simply prints the product of T and w without writing zero. 2) Check command erroneously concludes that index of the derivative of following scalar function is [i], whereas it should be none. diff(psi(G[i],theta),theta); Please refer to my post on http://www.mapleprimes.com/forum/maple-11-physics-package-indicial-notation-derivative-question for further details. 3) If one equates a tensor to zero, the Check command fails. Define(Q); eq:=Q[i]=0; Check(%); Error, (in Check) free indices in both sides of the equation are different: found {i} in the left-hand-side and {} in the right_hand-side I see this as a limitation. When equated to zero check command works only if the lhs of equation is a scalar. However, maple needs to allow equating equations with a free indices to zero as well, which is needed for many physical equations. I will keep updating this list, as I make progress in using this package. Others are welcome to update it by posting comments. Sincerely, Pawan Takhar Texas Tech University ﻿