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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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