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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: 01 Apr 2007 14:31:22 -0500

"Bill Page" <address@hidden> writes:

| On April 1, 2007 5:45 AM Gaby wrote:
| > 
| > >> Why should InputForm be preferable over Expression T?
| > >>
| > ... 
| > > For me to answer your question it is important to understand
| > > what Expression in Axiom really is. One way to do that is to
| > > look at the internal representation.
| > >
| > >  Rep:=Fraction SparseMultivariatePolynomial(T, Kernel %)
| > >
| > > So Expression is a mathematical domain of rational functions
| > > (ratio of two polymonials) where the polynomial variables
| > > are extended to kernels including various special functions.
| > 
| > Sorry, I don't think I'm satisfied with an answer that has to
| > look at the internal representation before explaining why I
| > should not believe the interface.
| >
| Of course you should believe the interface! There is no need to
| look at the internal representation.

I very much prefer an answer in terms of interfaces than that of
internal representation (where possible).  Because interfaces are what
explains the thingies to us -- even as developers.

| I just thought it might be
| easier since we are developers and are able to take a "white box"
| view.

I regret to say, but I'm a big fan of encapsulation (where useful) and
prefer to see interfaces even if I'm spending all my time tweaking in
the innards.  Thanks for the illustation. 

The difference, as I see it comes from the larger number of supported
mathematical operations for Expression T, than there are for InputForm.
Augment InputForm with all useful mathematical operations working on
InputForm and you'll see very little difference from Expression T.
Hence, Martin's warning.

Also, be aware than the Axiom designers, in many places, thought of
Expression as the general domain for symbolic manipulation and have
appropriate hardwired type inference rules in the interpreter.

-- Gaby

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