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## [Axiom-developer] [Axiom-mail] complex numbers

 From: Bill Page Subject: [Axiom-developer] [Axiom-mail] complex numbers Date: Wed, 29 Dec 2004 01:03:04 -0600

```Tim,

On Wednesday, December 29, 2004 2:28 AM you wrote:
>
> seems to be a categorical error of some sort.
>
> A: Complex Polynomial Integer
>
> tells the system that 'A' is expected to have a value which is
> Complex Polynomial Integer.
>
> 'conjugate' works on values, not potential values.
>
> Thus, conjugate(A) has no meaning as 'A' has no value.
> This should probably be an error.
>
> If axiom could work with so that conjugate worked on the type
> then axiom could work at some sort of an 'axiomatic' level
> rather than a symbolic computation level. Perhaps when we join
> forces with the ACL2 crowd we could state certain theorems and
> have them applied in the absence of a value.
>

I know that this is opening up the whole big subject again,
but I do think that Axiom is already "two-faced" about this.

Consider for example that we can write:

(7) -> A: Complex Polynomial Integer
Type: Void
(8) -> B: Complex Polynomial Integer
Type: Void
(9) -> A+B

(9)  B + A
Type: Complex Polynomial Integer

Neither A or B "has a value" but Axiom has no trouble agreeing
that A+B is still of type Complex Polynomial Integer.

I do not see any essential difference between this and

(10) -> A:Integer
Type: Void
(11) -> B:Integer
Type: Void
(12) -> A+B

A is declared as being in Integer but has not been given a value.

Regards,
Bill Page.

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