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

[Vladimir V. Kisil]

	Dear Alexey,

	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.
  (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.

  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). Thus we may think about a mechanism
  which will allow a GiNaC's user to choose the behaviour
  diff(abs). Shall it be some global boolean variable or something
  smarter?

  Another question: shall it be rigidly linked to a user's choice for
  an alternative behaviour of step function (as can be derived from your
  suggestion):

  step(0) = 1/2      or     step(0) = exception thrown.

  Thinking in this direction we can make GiNaC more flexible and useful.

  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 Wed, 17 Jun 2020 22:13:26 +0400, Alexey Sheplyakov <asheplyakov at yandex.ru> said:

    ASh> Hello,

    ASh> 17.06.2020, 21:54, "Richard B. Kreckel via GiNaC-devel"
    ASh> <ginac-devel at ginac.de>:
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    >> fa1ffcfdc9da97a6fb7cc2c9c36fe1fc45c808a9 (commit)       from
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    >> commit fa1ffcfdc9da97a6fb7cc2c9c36fe1fc45c808a9 Author:
    >> Pierangelo Masarati <pierangelo.masarati at polimi.it> Date: Wed Jun
    >> 17 19:52:49 2020 +0200
    >> 
    >>     Improve diff(abs(x)) for real x.

    ASh> I think this patch is wrong and should be reverted.
    ASh> diff(abs(x)) does not exist at x -> 0.  Alternatively one can
    ASh> modify the definition of numeric::step() function [1] so it
    ASh> throws an exception when being evaluated at 0.

    ASh> [1]
    ASh> https://www.ginac.de/ginac.git/?p=ginac.git;a=blob;f=ginac/numeric.cpp;hb=HEAD#l1070

    ASh> There's no way to "patch" math.

    ASh> Best regards, Alexey

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