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Re: [Axiom-developer] fixing SPAD

From: Waldek Hebisch
Subject: Re: [Axiom-developer] fixing SPAD
Date: Sat, 19 May 2007 16:01:17 +0200 (CEST)

Martin Rubey wrote:
> Dear Gaby & Waldek,
> as you may know, there is a problem fixing bug #354, Complex R is not
> necessarily a field when R is a field.
> It would be quite straightforward to fix it, if we could conditionally export
> Field, depending on a Boolean valued function, like
> if R has Field and R has Finite and size()$R rem 4 = 1 then Field
> Currently, spad seems to accept statements of the form
>    D has C
> and
>    D1 is d2
> only.  (Please check this, I'm not entirely sure.)  Do you think it would be
> difficult to fix this?  I do not see a workaround, unfortunately.

For issue 354 I belive that there is reasonable workaround: just export
Field unconditionally (as we do know), but throw error when sombody
tries to create a fake field.  For example PrimeField is doing this --
it exports Field for any value of p, but complains if you give it
non-prime p.

I belive that we should add to Complex something like the snippet below
(untested, ATM I am busy with other things)

   == add
      if R has Field then
         if R has complex or _
            ((characteristic()$R) mod 5 = 1) or _
            (R has Finite and _
               ((size()$R) mod 5 = 1) then
           error "Field given to Complex already contains square root of -1"

                              Waldek Hebisch

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