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Re: [Axiom-developer] Re: symbolic manipulation of expressions in Axiom

From: Gabriel Dos Reis
Subject: Re: [Axiom-developer] Re: symbolic manipulation of expressions in Axiom
Date: 02 Apr 2007 10:14:55 -0500

Waldek Hebisch <address@hidden> writes:

| Gabriel Dos Reis wrote:
| > "Bill Page" <address@hidden> writes:
| > 
| > [...]
| > 
| > | I would like to discuss this more with other active Axiom
| > | developers.
| > 
| > Why should InputForm be preferable over Expression T?
| > 
| When I want use symbolic domain (which is rather rare) I want
| a single domain.  So one should fix T first.

Of course, you would have to fix T, but I put T there to emphasize
that you can fix it to whatever value pleases you.

|  Natural candidate for T is Integer.  But Expression Integer is a field of
| characteristic 0. 

and if you look at what other CASes have been using as symbolic
expression, you'll see that most of the time they assume field laws --
with ad-hoc rules when they realize something fishy is going on.  

| I can easily imagine expresions which go
| beyond that (noncommutative variables, zero divisors, mixed
| characteristic). 

Of course, but then you just rediscover many of the problems other
CASes run into.  Remember, the original issue is how to get an Axiom
domain to emulate symbolic computation (as done in other CASes).

| Also ATM Expression Integer does not do
| zero test before division but IMHO this is a bug. 


| OTOH  general symbolic domain may lack normal forms.

Yes, that is precisely why CASes implement "generalized" polynomials
as symbolic expression domains and augment it with ad-hoc rules.

-- Gaby

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