Re: [Axiom-mail] A newby question about eval and Expression

[Doug Stewart]

Martin Rubey wrote:

> Dear Doug,
>
> there are two issues in your code:
>
>
> Doug Stewart writes:
>
>  
>
> > )clear all
> > digits 20
> > -- n:=x^3+a1*x^2+a2*x+a3 ::Polynomial Fraction Integer
> >
> > Q:=(3*a2-a1^2)/9
> > R:=(9*a1*a2-27*a3-2*a1^3)/54
> > S:=(R+(Q^3+R^2)^(1/2))^(1/3)
> > T:=(R-(Q^3+R^2)^(1/2))^(1/3)
> > x1:=S+T-a1/3
> >    
>
> note that x1 is *not* a polynomial. Not even a rational function.
>  
>
>  

But it is a constant ---- How can I tell axiom that it is a constant?
I tried this way but :-(
)clear all
digits 20
-- n:=x^3+a1*x^2+a2*x+a3 ::Polynomial Fraction Integer

a1:=1
a2:=1
a3:=1

Q:=(3*'a2-'a1^2)/9
R:=(9*'a1*'a2-27*'a3-2*'a1^3)/54
S:  Complex Float :=(R+(Q^3+R^2)^(1/2))^(1/3)


I thought that if I gave a1 a2 a3 some in integer values, that Maxima 
would then know that it was a constant but no it thinks it is a variable????



> However, if you *can* avoid this domain (often you can't), try to do so, since
> it has a major drawback:
>
> A computer cannot test reliably whether some element of Expression Integer is
> zero or not. Axiom tries, but often fails. For example, the first example above
> is not zero for Axiom...
>
> (MuPAD, Mathematica and Maple try harder, but they often fail, too)
>
> Note that this problem does not arise for many other domains: you can test for
> zero in
>
> Integer,
> Polynomial Integer,
> AlgebraicNumber,
> PrimeField 5
> Matrix Integer,
> Fraction Polynomial PrimeField 1783
>
> and so on.
>
> Martin
>
>
>  
Thanks for your help, It clarified what I was seeing.  --- a big mess of 
numbers that was realy zero.

Doug Stewart