Dear Alexey,
On Wed, 17 Jun 2020 02:21:37 +0400, Alexey Sheplyakov <asheplyakov@yandex.ru> said: ASh> 17.06.2020, 00:30, "Vladimir V. Kisil" <v.kisil@leeds.ac.uk>: >> Dear Developers, >> To support Pierangelo's suggestion from here: >> https://www.ginac.de/pipermail/ginac-list/2020-June/002301.html
ASh> I'm afraid the patch is wrong. abs(x) is not differentiable at ASh> x = 0, and there's no way to "fix" that. ASh> x*abs(x) is differentiable at x = 0 (with derivative being ASh> zero). Unfortunately GiNaC can't automatically compute ASh> that. For now one can manually substitute x^2 -> abs(x)^2 which ASh> will reduce x^2/abs(x) + abs(x) to 2*abs(x) Without arguing on can we regularise the derivative abs(x) at x=0 by _declaring_ it being 0 or we cannot, I am missing you next argument. How does it speak against the patch? With this patch I have (in PyGyNac, sorry): In [1]: x=realsymbol("x") In [2]: e=x*abs(x) In [3]: print(e.diff(x)) {|x|}+ {(-1+2 \mbox{step}(x))} x In [4]: print(e.diff(x).subs(x==0)) 0 So we got exactly the value you have pointed out! 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