[GiNaC-list] Performance of simplify_indexed on long chains of Dirac matrices
Vladimir V. Kisil
kisilv at maths.leeds.ac.uk
Sun Jan 4 20:36:41 CET 2015
>>>>> On Sun, 04 Jan 2015 18:53:51 +0100, Vladyslav Shtabovenko <v.shtabovenko at tum.de> said:
VSh> 1) By repeatedly applying the anticommutation relations to move
VSh> g_mu through all other matrices to g^mu. This is the easiest
VSh> but also the slowest way to implement.
This is what GiNaC is using, as far as I understand.
VSh> (people mostly care only about traces), it might be reasonable
VSh> to look at the performance of dirac_trace instead.
IMHO, this routine still uses clifford::eval_ncmul(), which I think
is the principal bottleneck.
VSh> takes around 5 seconds on my machine, a similar code with FORM
VSh> requires less than 0.01 seconds. With FeynCalc
Probably, GiNaC will never do a particular task as good as
a specialised software. GiNaC allows to mix all types of objects in a
single expression, so all simplifying algorithms need to be of a very
plain generic nature.
VSh> So I think that it would be very nice if someone of the GiNaC
VSh> developers could have a look at this issue.
I am not familiar with Dirac matrices close enough to optimise the
performance beyond the simple anticommutation. It will be good if you can
come with some optimisation suggestions of clifford::eval_ncmul().
Best wishes,
Vladimir
--
Vladimir V. Kisil email: kisilv at maths.leeds.ac.uk
www: http://www.maths.leeds.ac.uk/~kisilv/
Book: Geometry of Mobius Transformations
http://www.worldscientific.com/worldscibooks/10.1142/p835
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