[GiNaC-list] Performance of simplify_indexed on long chains of Dirac matrices

Vladimir V. Kisil kisilv at maths.leeds.ac.uk
Sun Jan 4 13:29:41 CET 2015

	Dear Vladyslav,
>>>>> On Sun, 04 Jan 2015 00:48:23 +0100, Vladyslav Shtabovenko <v.shtabovenko at tum.de> said:
    VSh> I'm wondering about the performance of simplify_indexed applied
    VSh> to a long chain of Dirac matrices in D dimensions.

    You raised a valid concern. Let me provide some
  background. Historically, GiNaC was dealing with Dirac matrices
  associated to the Lorentz metric only. At some point the code was
  expanded to treat an algebra with a general commuting/anticommuting
  relation between generators. Since the generality reduced performance,
  the original code optimised for Dirac matrices was preserved as much
  as possible.

  I checked your example, it did not call to general time-consuming
  cliffordunit::contract_with(), canonicalize_clifford() and
  get_metric(). Instead, it (as it is supposed to do) made numerous
  calls to clifford::eval_ncmul() and diracgamma::contract_with(). I
  believe that the later two functions are mainly as they were in the
  original GiNaC code optimised for Dirac matrices.

  So, a further investigation of the code is required....

  Best wishes,
Vladimir V. Kisil     email: kisilv at maths.leeds.ac.uk
                        www: http://www.maths.leeds.ac.uk/~kisilv/
Book: Geometry of Mobius Transformations

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