[GiNaC-list] I want to Add Integrating by Parts in GiNaC Symbolic Integration

[Vladimir V. Kisil]

>>>>> On Thu, 1 Aug 2024 05:40:24 +0700, DS Glanzsche <dsglanzsche at gmail.com> said:

    DS> I was only going to follow Purcell' Calculus book or more or
    DS> less like the old formula for Integration by parts from
    DS> https://en.wikipedia.org/wiki/Integration_by_parts In
    DS> SymbolicC++ they are able to handle integration by parts for x *
    DS> exp(x).

    If you will manage a code which can handle all (or many) cases from
  this Wiki article, it will be very good. 

    DS> I am really naive and still in undergraduate books of
    DS> Mathematics I don't even know the Ostrogradsky's procedure.

    You can find it at many resources, in particular §4 of these notes:
http://v-v-kisil.scienceontheweb.net/courses/math0212-notes.pdf

-- 
Vladimir V. Kisil                  http://v-v-kisil.scienceontheweb.net
  Book:      Geometry of Mobius Maps       https://doi.org/10.1142/p835
  Soft:      Geometry of cycles         http://moebinv.sourceforge.net/
  Jupyter notebooks:        https://github.com/vvkisil?tab=repositories

>>>>> On Mon, 29 Jul 2024 19:51:56 +0700, DS Glanzsche
    DS> <dsglanzsche at gmail.com<mailto:dsglanzsche at gmail.com>> said:

    DS> I just learned about GiNaC, and I want to add integration by
    DS> parts for a bit of complex integration like integral of cos nx *
    DS> x, for definite and indefinite integral. I think polynomial
    DS> integration in GiNaC works amazing, but if we can add all other
    DS> symbolic integration it will be better.

    DS>     For integration by parts, the key step is to factorise f=u
    DS> ·v into a part for integration and a part for
    DS> differentiation. Do you know a good algorithm to make the
    DS> decision? (I would be interested to see it as a seasonal
    DS> lecturer of integral calculus as well)

    DS>   We definitely can implement the Ostrogradsky's procedure for
    DS> integration of rational functions because it is algorithmic and
    DS> we already have the necessary polynomial arithmetic for it.

    DS> Should I look and modify the source code integral.cpp? I never
    DS> really modified open source code before in my life.

    DS>     We all had this first moment in our life, hopefully you will
    DS> enjoy the process!  -- Vladimir V. Kisil
    DS> http://v-v-kisil.scienceontheweb.net Book: Geometry of Mobius
    DS> Maps https://doi.org/10.1142/p835 Soft: Geometry of cycles
    DS> http://moebinv.sourceforge.net/ Jupyter notebooks:
    DS> https://github.com/vvkisil?tab=repositories