On 19.07.23 17:31, '68th' via FriCAS - computer algebra system wrote:
I appreciate your help Professor Grabmeier. I must admit I'm
astonished to learn that we need tricks to do elementary algebra in a
computer algebra system.

Well, FriCAS maybe difficult for beginners and it may seem that one has to use a lot of tricks to do what one wants, but look for example through this

https://fricas.github.io/fricas-notebooks/FriCAS-SkewPolynomial.html

and try to achieve the same with another CAS. Or (we all know that taylor series form a ring T, squrae matrices of size 2x2 with entries being Taylor series also form a ring M. Can you create a structure that is a polynomial ring with in the variable x whose coefficients live in M? In FriCAS you can. You have to create all these rings, but it's possible. Try to do this in Maple or Mathematica. First of all, if I am not wrong, they do not have infinite Taylor series, only truncated ones. So you first have to program these.

So it all depends on what you want to use the CAS for. Some systems try to be generic, FriCAS is better at handling concrete algebraic structure. You can do fancy things with FriCAS that you might not even have learned in you mathematica curriculum yet. But for that you have to invest some time and understand how FriCAS is different from typeless CAS.

Ralf

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