Re: [Axiom-mail] complex numbers

[Bob McElrath]

root address@hidden 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.

Then it should not *appear* to work and should give an error: cannot
compute conjugate of indeterminate 'A'.

> 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.

Well... A + conjugate(A) is most definitely a Complex Polynomial
Integer, I don't think it requires a fully axiomatic approach to
understand or use that.  Maple, Mathematica, and Maxima all get this
right...

conjugate is a characteristic of the number itself, just as the negative
sign in negative numbers is not an operator but part of the number
itself.  (of course, one can implement it both ways...)

--
Cheers,
Bob McElrath [Univ. of California at Davis, Department of Physics]

    "It's not the people who vote that count. It's the people who count the
    votes." -- Joseph Stalin

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