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## [Axiom-developer] [Axiom-mail] (new) complex numbers

 From: Bill Page Subject: [Axiom-developer] [Axiom-mail] (new) complex numbers Date: Wed, 29 Dec 2004 00:37:16 -0600

```On Wednesday, December 29, 2004 1:17 AM Bob McElrath wrote:
>
> Andrea Bedini address@hidden wrote:
> > Hi,
> > I'm just learning how to do some computations with Axiom,
> > but I've a problem with complex numbers.
> >
> > Why this evalutate to zero ?
> >
> > (199) -> A: Complex Polynomial Integer
> >
>        Type: Void
> > (200) -> A*conjugate A - A^2
> >
> >    (200)  0
>
> Definitely wrong.  It looks like the source of the problem is:
>
> (18) -> conjugate(a)
>
>    (18)  a
>                                Type: Complex Polynomial Integer
>

Of course I agree that it is wrong. But what would you expect
the answer to be?

conjugate(a)

could return unevaluated as just

conjugate(a)

but then what should the Type: be? Is such an expression
still necessarily a Complex Polynomial Integer?

This is dangerously close to the discussion that we had some
months ago about the meaning of "indeterminants", objects
which have a type but no specific value. For example, I can
say

A:Integer

but if I write

A+1

If you answered "yes" to the idea that conjugate(a) is still
of type Complex Polynomial Integer, then surely A+1 is still
of type Integer is the same sense, but Axiom complains that
"A has not been given a value".

Perhaps evaluating the expression

conjugate(a)

should also complain about the lack of a value?

Regards,
Bill Page.

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