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## [Axiom-developer] [Axiom-mail] A newby question about eval and Expressio

 From: Doug Stewart Subject: [Axiom-developer] [Axiom-mail] A newby question about eval and Expression Date: Sun, 13 Nov 2005 21:01:06 -0600

```Changes http://page.axiom-developer.org/zope/mathaction/AxiomMail/diff
--
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

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