Thanks for that insight. I certainly like the Aldor language. I had always wished for a computer algebra package in Haskell, and Aldor seem to be just like that.
I think my confusion came from the "#include "fricas"", that you use when writing Aldor programs for use with Fricas, and that you can use some basic types like Integer (AldorInteger) interchangeably with the Fricas types. It was not clear to me if Fricas provided wrappers for most (all) of its functions for use within Aldor. So my current understanding is that there is some correspondence of the most basic types, that allows one to run the Lisp code generated by Aldor within Fricas. With respect to the series expansions, what I would like to understand is: Why does a simple series(0.1*x, x=0.0) not work, even with type annotations? This becomes relevant when I start with an expression Expression(Float) (maybe returned by some function) and want to series expand it. Maybe what you have written actually leads to an answer to that question, but it's not clear to me. Tobias On Wed, Jan 13, 2021 at 8:12 PM Ralf Hemmecke <[email protected]> wrote: > Hello Tobias, > > > Pure Aldor might be an interesting avenue. > > Yes, but it comes at a price. > > > For prototyping I will probably first use the interactive mode or > > SPAD and then think about pure Aldor vs. an ECL or pipe route. > > Well, it depends on what you want to do. If you want to use the > algorithms implemented in FriCAS, then the Aldor way is gone. > > Aldor is, in fact, a separate project. It is a compiler and a library > (actually several libraries). The libraries are not compatible with the > FriCAS library. > > What the Aldor-FriCAS interface does, is that it allows to use the aldor > COMPILER instead of the FriCAS compiler. Then you have to use Aldor > Syntax instead of SPAD syntax (there are a number of differences, > though). In effect, however, when you use the Aldor compiler in this > way, you generate lisp code for use in FriCAS, i.e. not a standalone > library. > > In other words, if you want to use the algorithms from FriCAS in your > program, then the Aldor route will not work. > > > Concretely I am interested in > > Puiseux series. Looking at the source, the Aldor algebra library does > > seem to have at least a Taylor series. To make it clear: as a first > > step I would be interested in writing Aldor programs (instead of > > SPAD) and load them in FriCAS (with ")compile"), so not standalone > > Aldor programs. > > See above. If you want a standalone library, then either > forget about FriCAS and use what you can find in the Aldor (algebra) > library or you must connect your program to FriCAS in some way and then > you can use everything from FriCAS. > > There is not Puiseux series implementation in the aldor library, but if > you look at how it is done in FriCAS, then it is clear that an > implementation is pretty easy. > > - Is UnivariatePuiseuxSeries(Expression(Float), 'x, 0.1::Float) > > something that is not well-defined, or is it just not implemented? -> > > series((0.1::Float)*x,x,0.0::Float) ... Cannot find a definition or > > applicable library operation named series with argument type(s) > > Polynomial(Float) Variable(x) Float > Maybe this gives yo an idea. > > (1) -> F ==> Float > (2) -> E ==> Expression F > (3) -> P ==> UnivariatePuiseuxSeries(E, 'x, 0.1::F::E) > (4) -> z := monomial(1,1)$P > > (4) (x - 0.1) > Type: UnivariatePuiseuxSeries(Expression(Float),x,0.1) > (5) -> z^3 > > 3 > (5) (x - 0.1) > Type: > UnivariatePuiseuxSeries(Expression(Float),x,0.1) > (9) -> 1/(1-z) > > (9) > 2 3 4 5 > 1.0 + (x - 0.1) + (x - 0.1) + (x - 0.1) + (x - 0.1) + (x - 0.1) > + > 6 7 8 9 10 > (x - 0.1) + (x - 0.1) + (x - 0.1) + (x - 0.1) + (x - 0.1) > + > 11 > O((x - 0.1) ) > > Ralf > > -- > 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 view this discussion on the web visit > https://groups.google.com/d/msgid/fricas-devel/1bcfcd50-3238-b3f5-0ea8-6b132edf18fe%40hemmecke.org > . > -- 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 view this discussion on the web visit https://groups.google.com/d/msgid/fricas-devel/CANL0awZvjn%3DStBfJPh-S-acOPbaw5pNN%2BpJngXYco9aGYJcsDA%40mail.gmail.com.
