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Software to calculate simple commutator relation ?

  1. Jun 11, 2009 #1
    software to calculate simple commutator relation ??

    Dear All:
    I have hundred terms of commutators needs to be calculate. Each one looks like
    [{\epsilon_{i m}}^n\eta^m\frac{\partial}{\partial\eta^n},C\eta_j\eta^l\frac{\partial}{\partial\theta^l}]
    [/itex] ,where C is function of [itex]\theta^i[/itex] and [itex]\eta^i[/itex].
    The result of this commutator is
    {\epsilon_{im}}^n\eta_j\eta^m\frac{\partial C}{\partial\eta^n}\eta^l\frac{\partial}{\partial\theta^l}-C\epsilon_{ijm}\eta^m\eta^l\frac{\partial}{\partial\theta^l}+
    Is there any software can deal with this calculation and preserve the Einstein summation convention?
    I have try to use a mathematica note book from http://www.commeare.net/2008/05/03/commutator-relations-in-mathematica/ [Broken]
    to calculate the component of the commutator ie. take i=1 j=2 for example, but mathematica 's simplification rule make the result hardly to read.
    Any help will be appreciated. Thanks.
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Jun 11, 2009 #2


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    Science Advisor

    Re: software to calculate simple commutator relation ??

    Cadabra might be of some help...

    http://www.aei.mpg.de/~peekas/cadabra [Broken]

    One of the "sample notebooks" on the website shows how to
    simplify some commutators using the example of the
    Poincare algebra. But you'll probably need to study the
    reference manual and other examples (and maybe get a bit
    of help from Cadabra's author) if you've got hundreds of
    commutators to deal with.
    Last edited by a moderator: May 4, 2017
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