On Thu, Oct 30, 2008 at 8:39 AM, Alejandro Jakubi wrote:
> I wonder how it is done in Axiom the selection of roots of a polynomial
> with some property. As in this example, select the positive roots out
> of the list of three roots generated by:
>
> radicalSolve(p^3-p+1/10=0,p)
>
Since the discriminant is positive we know all roots are real, so in
principle we should be able to solve the problem like this:
(1) -> discriminant(p^3-p+1/10)
373
(1) ---
100
Type: Fraction(Integer)
(2) -> select(p+->rhs(p)::AlgebraicNumber>0,radicalSolve(p^3-p+1/10=0,p))
+------------------+2
| +-+ +-----+
+---+ |- 3\|3 + \|- 373
(- 3\|- 3 - 3) |------------------ + 2
3| +-+
\| 60\|3
(2) [p= -----------------------------------------]
+------------------+
| +-+ +-----+
+---+ |- 3\|3 + \|- 373
(3\|- 3 - 3) |------------------
3| +-+
\| 60\|3
Type: List(Equation(Expression(Integer)))
---------
As I understand it AlgebraicNumber is supposed to be able to properly
order the roots. Unfortunately there seems to be a bug and
AlgebraicNumber gets it exactly wrong!
(3) -> complexNumeric rhs %.1
(3)
- 1.0466805318 0460226115 8656311996 0435287484 7096514654 44382606
+
- 0.6 E -60 %i
Type: Complex(Float)
The actual positive roots are:
(4) -> select(p+->rhs(p)::AN<0,radicalSolve(p^3-p+1/10=0,p))
(4)
+------------------+2 +------------------+2
| +-+ +-----+ | +-+ +-----+
+---+ |- 3\|3 + \|- 373 |- 3\|3 + \|- 373
(- 3\|- 3 + 3) |------------------ - 2 3 |------------------ + 1
3| +-+ 3| +-+
\| 60\|3 \| 60\|3
[p= -----------------------------------------,p= ---------------------------]
+------------------+ +------------------+
| +-+ +-----+ | +-+ +-----+
+---+ |- 3\|3 + \|- 373 |- 3\|3 + \|- 373
(3\|- 3 + 3) |------------------ 3 |------------------
3| +-+ 3| +-+
\| 60\|3 \| 60\|3
Type: List(Equation(Expression(Integer)))
------
Regards,
Bill Page.
-------------------------------------------------------------------------
This SF.Net email is sponsored by the Moblin Your Move Developer's challenge
Build the coolest Linux based applications with Moblin SDK & win great prizes
Grand prize is a trip for two to an Open Source event anywhere in the world
http://moblin-contest.org/redirect.php?banner_id=100&url=/
_______________________________________________
open-axiom-devel mailing list
open-axiom-devel@lists.sourceforge.net
https://lists.sourceforge.net/lists/listinfo/open-axiom-devel
