Which Computational Software Is Best for Tensorial Hermite Polynomials?

[parulm]

I need to use a computational software to work on tensorial hermite polynomials. The operations I want to perform are complex combinations of integration, summation and permutation over indices. Please refer to this image: https://www.dropbox.com/s/2ogp4mr7ejg7x8o/Screenshot 2014-07-07 19.49.16.png
For example, in the above, I want to be able to compute the expression for the expansion coefficient for given n as is done manually in the image below: https://www.dropbox.com/s/2ogp4mr7ejg7x8o/Screenshot 2014-07-07 19.49.16.png
Also, at later stages, I will be using tensor contraction, inner product very often, so I need the software to have good support for the same.

Thanks!

 

[jedishrfu]

Your best bet is either Mathematica or MATLAB. Mathematica can do symbolic math and numerical solutions whereas MATLAB is geared primarily for numberical solutions.

A mathematica summary of features:

http://en.wikipedia.org/wiki/Mathematica

and MATLAB

http://en.wikipedia.org/wiki/Matlab

Alternatively, you could consider Freemat or Octave as free clones of MATLAB with the same core features for numerical computation.

Here's a list / comparison of other numerical software packages:

http://en.wikipedia.org/wiki/Comparison_of_numerical_analysis_software

and lastly here's a list / comparison of symbolic math packages:

http://en.wikipedia.org/wiki/Comparison_of_computer_algebra_systems

 

[George Jones]

I use Maple for symbolic tensor calculations in general relativity. I like it, and I find that it does what I need (I don't know about your needs, though), but the main reason that I use it is that my employer has a site license, so I have Maple freely and legally installed on my computers.

 

[parulm]

Dear George,

Thanks! Can we interchange indices of a tensor in Maple. Or maybe get a permutation. For example, get A_ij from A_ji or get B_ijk and B_ikj etc from B_jki? I am using a software called maxima right now which is very much like mathematica and I cannot figure out a way to get permutations in that.