Hi Ralf, Thank you! I did not know that wiki page exists. I am familiar with
http://axiom-wiki.newsynthesis.org/SandBoxNoncommutativePolynomials It would be great if the articles in the wiki were organized in categories (which is the most natural thing for FriCAS wiki!). Then it would be easy to find all articles related to noncommutative polynomials. Actually, the operators that I want are very similar to sin(x). I took a look at elemntry.spad and I defined my own operator, just like sin, in myop.spad, compiled it, exposed it and when I tried to use it, FriCAS said that there is no such operator. How should I do it? > If you tend to use expressions and maybe the "rule" and "ruleSet" > facilities, then I would claim that you use FriCAS just as a symbolic > manipulator Agreed. Reading the FriCAS book I have come to realize that there is a difference between symbolic manipulation and computer algebra. I have some experience doing what you said with Maxima and it is very awkward. One of the first things I did with FriCAS was this: sum(k,k=1..n) n² + n ------ 2 sum(k,k=1..n) :: Fraction Factored Polynomial Integer n(n + 1) -------- 2 This shows the elegance and power of mathematics! Unfortunately, the way mathematics is taught and used by many physicists amounts to just doing symbolic manipulations, which makes it very hard to understand for both students attending their lectures and peers reading their papers. Moreover, the above type conversion affords the separation between declarative and imperative that is so little appreciated by scientists and programmers alike. The type conveys the information necessary to understand what happens to the first expression while hiding how it is done. > You must change your mindset away from just expression tree > manipulation. The right way for FriCAS is to think about what the > algebraic structure of your operator algebra is and then program a > domain for it. That is precisely my goal :) In recent years I have given some thought to the design of a CAS and I am beginning to realize that what I want to do comes very close to FriCAS. At some point I want to start writing packages and share them with colleagues. I believe the TeXmacs+FriCAS combo can become a huge time-saver. Thanks for the pointers to the Lie algebra-related domains. I had looked at them and got the impression they are more matrix-oriented than symbolic-oriented. Marduk -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
