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.

 

[blue_raver22]

I would recommend using a specialized computational software such as TensorFlow or PyTorch for working with tensors and tensorial hermite polynomials. These software packages have built-in functions for complex combinations of integration, summation, and permutation over indices, making it easier to perform operations such as the expansion coefficient calculation shown in the provided image. They also have good support for tensor contraction and inner product, as mentioned in the request. Additionally, these software packages are widely used and have a large community of users, making it easier to find resources and support. Other options could include MATLAB or Mathematica, which also have robust tensor capabilities. Ultimately, the best software to use will depend on your specific needs and preferences, so I would recommend exploring different options and choosing the one that best fits your research goals.