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Which software to use? #tensors

  1. Jul 7, 2014 #1
    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!
     
  2. jcsd
  3. Jul 8, 2014 #2

    jedishrfu

    Staff: Mentor

    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
     
  4. Jul 8, 2014 #3

    George Jones

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    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.
     
  5. Jul 9, 2014 #4
    Dear George,

    Thanks! Can we interchange indices of a tensor in Maple. Or maybe get a permutation. For example, get Aij from Aji or get Bijk and Bikj etc from Bjki? 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.
     
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