Re: [fricas-devel] Re: [Axiom-math] Selection of roots

[Alejandro Jakubi]

On Mon, 3 Nov 2008, Bill Page wrote:

> Why, that's almost there! :-)  I agree that tutorial documentation is
> a problem. If you haven't already seen it, perhaps you would be
> interested in:
>
> http://axiom-wiki.newsynthesis.org/RealClosure
>
> Especially the paper: axiom-field.pdf

Yes, it will be very useful. In particular to aid a bit with the mathematical
jargon used so intensivelly in Axiom, that is a bit cryptic to a Physicist like 
me.

> One thing that would be very useful is if someone like you were able
> to contribute some documentation like this that could be added to the
> axiom-wiki and perhaps also the Axiom book.

May be. But wait. I am slow and it takes me a very long time to understand
these kind of things. At present I do not understand even the basics of the
Axiom system. And I do not find sensible that try contributing to this
documentation until I beleive that I understand the subject enough.

You see, it is over 15 years that I am using Maple, and it is only now that I
feel that I understand enough about a few subjects to begin writing on them in 
the
Maple wiki (http://mapleadvisor.com/cgi-bin/moin.cgi/StartingPage)

> BTW, what is you basic
> source of information about Axiom?

I think that there is nothing that I could call a basic source of information
about Axiom.

For several years I have been collecting all sort of documentation, including 
the
Axiom book (in different versions, formats, etc), tutorials, posts to the
lists, wiki pages, etc.

And now I have began trying to "decode" the output of commands like ')show'
(without much success yet).

In most cases, none of them by itself, provides an answer to my howto
questions. Hence, currently, I am collecting such dispersed bits of
information plus examples in TeXmacs sessions to help orient myself in this
search.

> I believe that all you are really interested in are the roots of the
> numerator of the expression (provided of course that they are not also
> roots of the denominator), right?

Right.

> (3) -> S:=allRootsOf(numer fp)$RealClosure(Fraction Integer)
>
>   (3)  [%A9,%A10]
>                                      Type: List RealClosure Fraction Integer
> (4) -> approximate(S.1,1/10^20)::Float
>
>   (4)  - 6.7957899636 620037966
>                                                                  Type: Float

The final step in these examples would be to recover the algebraic expression
of these selected roots (instead of a float evaluation).

Alejandro Jakubi