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Re: [Axiom-developer] Question concerning types...

From: Gabriel Dos Reis
Subject: Re: [Axiom-developer] Question concerning types...
Date: 17 Sep 2006 02:14:26 +0200

C Y <address@hidden> writes:

| --- Gabriel Dos Reis <address@hidden> wrote:
| > | Wouldn't that information be associated with the variable n?
| > 
| > but "n"'s type isn't Variable(some type), it is "some type", meaning,
| > it holds *values* of that type.
| OK.
| > But you want it to hold a token of some type.  That is a different
| > story.
| Surely that isn't a surprising way to want to use a CAS?

Not really.  You did not say you wanted "n" to be a symbol; you want
it to designate some *value*.

| I'm actually surprised something like a1 : Integer would be handled any
| other way then as a token with type, but again that may just be me not
| knowing enough.

There is a difference between a symbol and an Integer.

What you want, if I understand your manipulation correctly, is to use
symbols, and only later subsitute some values for those symbols.  And
you want to make sure that the symbols are interpreted in some ways.
But, you can't say that directly in the Axiom type system.  Because
Axiom does not attach advanced types to symbols.

| > With systems that do "symbolic" manipulations, you don't get that
| > trouble; with with systems like Axiom that do actually computations,
| > you have to go through an additional indirection.
| I'm not sure I'm totally clear on the distinction.  After all, Axiom
| can do things like integrate(1/(1+x^4),x) and provide a result - how is
| that not a symbolic manipulation?

Yes.  Notice that in that context "x" is interpreted as *symbol*, not
as a value.  Your declaration of "n" said it should be interpreted as
standing for a value, but you did not say which.

-- Gaby

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