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

[DS Glanzsche]

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


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

I am really naive and still in undergraduate books of Mathematics I don't
even know the Ostrogradsky's procedure.
Thanks for the information, I will try my best and hopefully I can make
integration by parts with GiNaC.

Le lun. 29 juil. 2024 à 21:46, Vladimir V. Kisil <V.Kisil at leeds.ac.uk> a
écrit :

> >>>>> On Mon, 29 Jul 2024 19:51:56 +0700, DS Glanzsche <
> 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.
>
>     For integration by parts, the key step is to factorise f=u ·v into a
>   part for integration and a part for differentiation. Do you know a
>   good algorithm to make the decision? (I would be interested to see it
>   as a seasonal lecturer of integral calculus as well)
>
>   We definitely can implement the Ostrogradsky's procedure for
>   integration of rational functions because it is algorithmic and 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.
>
>     We all had this first moment in our life, hopefully you will enjoy
>   the process!
> --
> 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
>
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