[GiNaC-devel] [SCM] GiNaC -- a C++ library for symbolic computations branch, master, updated. release_1-4-0-659-gfa1ffcfd

[Vladimir V. Kisil]

	Dear All,

	Alexey's proposition of an additional method for regularised
  derivative seems to be reasonable and shall not be difficult to
  implement. Actually we can have all of them: left_diff, right_diff and
  mean_diff. For many functions these will be the same as diff anyway. 

  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: https://github.com/vvkisil/MoebInv-notebooks
>>>>> On Thu, 18 Jun 2020 00:27:33 +0400, Alexey Sheplyakov <asheplyakov at yandex.ru> said:

    ASh> Vladimir,

    ASh> 17.06.2020, 22:58, "Vladimir V. Kisil" <v.kisil at leeds.ac.uk>:

    >>         I think the statement 'no way to "patch" math' is too
    >> strong:   there are many examples of such patches. Say, the
    >> singular integral of   f(x)/(x-t) over the real line is
    >> divergent, but is meaningful (and   useful) for "the Cauchy's
    >> principal value". Cesàro summation, Abel   summation, and many
    >> others summations are examples of patches   for divergent series.

    ASh> Not really. They are *different* mathematical entities.

    >>   (Not even speaking about examples like: 1+2+3+4+5+... = -1/12
    >> .)
    >> 
    >>   Similarly it is quite legitimate (and useful in some
    >> circumstances) in   some cases to regularise a piece-wise
    >> differential function by assigning   the derivative to be the
    >> mean of the left and the right derivatives.

    ASh> There's nothing wrong with that. As long as the user (not
    ASh> GiNaC) is in control which definition is being used. So if the
    ASh> user asks for a plain derivative, and it does not exist, GiNaC
    ASh> should prominently report that (throw an exception) instead of
    ASh> trying to choose a different definition of the derivative to
    ASh> "fix" the problem.  It's OK to define an extra method
    ASh> (`regularised_diff', whatever).  But "smart" adjustments of
    ASh> plain `diff' are not OK.

    ASh> Such "smartness" is the major reasons why I dislike "real"
    ASh> computer algebra systems.

    >>   The possible argument is that sometimes this regularisation may
    >> be   misleading (I do no have a sound example in my head for this
    >> but can   admit it potential existence).

    ASh> In high energy physics (the original domain of GiNaC)
    ASh> expressions (Green functions, scattering amplitudes) are often
    ASh> divergent. I guess nothing will get wrong due to "improved"
    ASh> abs.diff(). Until someone decides to "improve" tgamma(x) at x =
    ASh> 0 in a similar manner.

    ASh> That said, these days (high energy) physics is a hobby for me.
    ASh> I rarely compute Feynman diagrams, and I've got no deadlines.
    ASh> So I don't care that much. If GiNaC will become too "flexible
    ASh> and smart" I can switch to a different library (or even roll
    ASh> another one from the scratch).

    ASh> Best regards, Alexey
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