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Re: [Axiom-developer] Zero divisors in Expression Integer

From: Francois Maltey
Subject: Re: [Axiom-developer] Zero divisors in Expression Integer
Date: 17 Jan 2007 22:20:35 +0100
User-agent: Gnus/5.09 (Gnus v5.9.0) Emacs/21.4

Dear Waldek,

Thanks a lot for your previous accurate reponse.

It seems you understand what I'm looking for, 
and  I hope understand how you want axiom computes. 

> I want Axiom to produce mathematically correct results.  
> [and use] algebraic interpretation otherwise we get wrong results.

> To handle conventions used in calculus we need higher
> level packages.

> But the case analysis may get messy (after all the problem is
> undecidable) and will have to give up (say return expression 
> unevaluated).

For students I must have a minimal analysis point of view.

It's right, axiom can have both points of view with (many) domains.
    1/ algebraic domains which are really right 
and 2/ others domains for usual calculus, less perfect but more usual...

> This is impossible if you want to stay in a single domain.
> [I cut the two pretty examples with exp and log]
> So really each Axiom domain must implement its on simplifications.

I agree, I recognize I forget this notion when I began to study elemntry.spad.

> Have you thought how your work fits into Axiom design? 
First I thought it was the aim of Expression.
But now I recognize it's perhaps a bad idea.

Hi Everybody ! 
Do you have any idea about calculus domain for easy computation 
as Maple, mupad and other Texas pocket calculators ?

Do you have an .axiom.input for students and professors ?

By example my students don't know the minimal polynomial for algebraic number,
so the reponse true for this calculus is too curious : 

[axiom] a := 3 + sqrt 5 ; test ((a^2)^(1/2)=-a)   --- the reponse is true

So for theses computations I pefer to use RealClosure than AlgebraicNumber ;
and I expect to have a smaller axiom, but a consistent system.

Please, give me some advices !


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