[GiNaC-devel] Power laws

[Vladimir V. Kisil]

	Dear Richard,
>>>>> On Tue, 15 Oct 2019 09:23:21 +0200, "Richard B. Kreckel" <kreckel at in.terlu.de> said:
    RK> Well, after celebrating this patch, we should discuss it
    RK> breaking check/exam_paranoia.cpp:217.

    RK> That particular check has nothing to do with the exp() function,
    RK> so we could re-write it in terms of Li2() or some other function
    RK> and be done with it.

    RK> But François Maltey objected about exp(x)/exp(x) not eval'ing to
    RK> 1 any more:
    RK> https://www.ginac.de/pipermail/ginac-devel/2009-October/001680.html

    RK> And, somehow, that should be addressed, I guess.

    It seems that both mentioned issues are connected. I am attaching a
  revised patch which applies the law of exponents, but keeps exp(x)^(-1) as
  exp(x)^(-1). With this patch check/exam_paranoia.cpp (as well as all
  other checks) went well (at least on my computer.)

    RK> I propose
    RK> writing generic functions outside the automatic eval system
    RK> along these lines https://www.ginac.de/FAQ.html#treetraverse
    RK> searching for common arguments of exp() which may be
    RK> combined. Would you like to venture?

  I will keep thinking on implementation of the rule e^t * e^s = e^(t+s).
  At the moment, I am in a favour to make it a part of a more general
  mechanism which will allow a user to apply some specific
  transformations for particular functions on demand (beyond wildcard
  substitutions). So it will not be done with the automatic evaluation
  and will not slow down the traditional performance. May be it is worth
  to add some more properties like add_func(), mul_func(), ncmul_func()
  to complement the existing power_func()... 

  Best wishes,
  Vladimir
-- 
Vladimir V. Kisil                 http://www.maths.leeds.ac.uk/~kisilv/
  Book:     Geometry of Mobius Transformations     http://goo.gl/EaG2Vu
  Software: Geometry of cycles          http://moebinv.sourceforge.net/
  Jupyter (Colab):         https://github.com/vvkisil/MoebInv-notebooks
  Jupyter (CodeOcean):       https://codeocean.com/capsule/7952650/tree

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