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Re: [Axiom-developer] fixing SPAD

From: Martin Rubey
Subject: Re: [Axiom-developer] fixing SPAD
Date: 19 May 2007 19:53:12 +0200
User-agent: Gnus/5.09 (Gnus v5.9.0) Emacs/21.4

Waldek Hebisch <address@hidden> writes:

> > In any case, I thought that Complex R is intended to be the ring of formal
> > linear combinations of 1 and %i, where %i^2 = 1.  (That's also roughly what 
> > the
> > doc says.)  Do you see a different interpretation for the 'Complex'
> > constructor?

> I view Complex as a special purpose constructor: square root of -1
> has distinguished role for subsets of complex numbers.  

But I wouldn't consider Complex PF 3 as a subset of the complex numbers, since
the arithmetic is different. 

> But in general one wants arbitrary algebraic extensions, and
> SimpleAlgebraicExtension provide them (well, as long as R is commutative),
> without special assumptions hardwired into Complex.

Looking at SAE, I see that it exports Field if its underlying ring is a Field.
I guess we have a problem there, too?

> Note also that you need to be _very_ carefull when you work with rings having
> zero divisors.

I would like to trap zero divisors with the predicate 

  if R has Field then ...


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