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

From: C Y
Subject: Re: [Axiom-developer] Question concerning types...
Date: Sat, 16 Sep 2006 20:57:06 -0700 (PDT)

--- Gabriel Dos Reis <address@hidden> wrote:

> | > 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*.

Yes and no.  I want it to be a variable, but a variable of a specific
type.  So rather than just saying x is "something" I say it is "some
integer" or "some float".  I thought I was saying that, but apparently
not - do I understand correctly that what I thought I was saying in
fact cannot be said in Axiom at this time?

> 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.

Is there a reason it does not, or is just something that hasn't been
> 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.

So what I want then, using your terminology, would be a way to declare
a symbol to have a Type.  The reason a1 : MachineInteger produces the
expectation of a value is that Axiom simply doesn't support a symbol
with a Type, and so that assignment carries with it the assumption that
a1 now has some specific value?

Ouch.  There are many cases where one tries to solve a problem to
arrive at a symbolic equation, not a value.  If Axiom makes this
difficult that's going to be a real problem.

As long as I'm asking basic questions, just how would I go about
defining a function f(x) that took the expression produced by
integrating(1/(1+x^4),x) and numerically evaluated it for the given
value of x?  


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