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@leeds.ac.uk> a écrit :
On Mon, 29 Jul 2024 19:51:56 +0700, DS Glanzsche < dsglanzsche@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