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
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