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

[Bill Page]

On Mon, Nov 3, 2008 at 1:32 PM, Martin Rubey wrote:
>
> "Bill Page" <address@hidden> writes:
>
>> As I understand it AlgebraicNumber is supposed to be able to
>> properly order the roots.
>
> No, that's RECLOS.
>
> Unfortunately, there is no coercion from AN to RECLOS, and this would
> actually be tricky, since sqrt(-3) is not allowed in RECLOS.
>

Thanks Martin, that was a very useful reference. Actually it turns out
that RealClosure is pretty cool.

Thank you Renaud!

(1) -> P:=p^3-p+1/10

         3        1
   (1)  p  - p + --
                 10
                                    Type: Polynomial Fraction Integer

(2) -> S:=select(positive?,allRootsOf(P)$RealClosure(Fraction Integer))

   (2)  [%A36,%A37]
                                    Type: List RealClosure Fraction Integer

(3) -> approximate(S.1,1/10^20)::Float

   (3)  0.1010312578 8101081769
                                     Type: Float

(4) -> eval(P,p=%)

   (4)  0.3 E -20
                                     Type: Polynomial Float

(5) -> approximate(S.2,1/10^20)::Float

   (5)  0.9456492739 2359144347
                                      Type: Float

(6) -> eval(P,p=%)

   (6)  0.1 E -20
                                       Type: Polynomial Float

----

Regards,
Bill Page.