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[Axiom-developer] Re: conditionally defined functions
From: |
Martin Rubey |
Subject: |
[Axiom-developer] Re: conditionally defined functions |
Date: |
Mon, 20 Sep 2004 13:38:09 +0000 |
William Sit writes:
> > In principle, this is not too difficult. However, there is a slight
> > subtlety:
> > Currently not all domains that contain variables provide such a function,
> > in
> > particular, FRAC does not. Instead, there is a package RF that provides
> > this
> > functionality. Well, no problem:
> >
> > * move the operation variables from RF and POLYCATQ to QFCAT :
> >
> > if S has variables: S -> List Symbol then
> > variables: % -> List Symbol
> > variables f ==
> > mymerge(variables(numer(f)), variables(denom(f)))
> >
> > and add the following to UP and MPOLY :
> >
> > if R has variables: R -> List Symbol then
> > coerce(r:R):% ==
> > if member?(x, variables(r)) then
> > error "coefficient contains variable"
> > else coerce(r)$Rep
> >
>
> If this works, it works wrongly, because this confuses the x in the inner
> domain of a tower with the x in the outer domain of the tower.
I don't understand what you mean with "wrongly". I'm aiming at the following: I
want that UP(x, FRAC POLY INT) or UP(x, EXPR INT) would be a rational function
(or expression) that is a polynomial in x. I tested the code above and it does
indeed "work" (in this sense).
> Remember that the compiler distinguishes these already. So the condition
> member?(x, variables(r))
> would always return false.
No, it does not. (at least not in the tests I ran)
> I don't know what you meant by "fishy". The code would not work at present
> because I don't think you can consider a function as an attribute.
Hmm, I think you can. The code above does so.
> The problem you raised is one of what might be called dynamic signature,
> that is
> the codomain depends on the input value. The Axiom compiler can handle this
> partly, in a category/domain constructor's signature, but not on the function
> level.
Yes, that's what I think, too.
> > So, in more general terms, here's my question:
> >
> > Suppose you have a category A, taking as parameter a domain P and
> > providing an
> > operation f: % -> P. Furthermore, you have a category (or a domain, a
> > package)
> > B, taking as parameter a domain Q. Now you want to achieve the following:
> >
> > If Q is a domain in A, provide a function g: % -> P, using f.
> >
> > Of course, it is not possible to provide P as a parameter of B, since B
> > should
> > also be defined for Q's that are not domains in A...
>
> The way to handle this is to create a special version of B, which takes a
> domain
> in A as parameter, together with parameters needed for A and construct the
> special version using the general one. This is ok because the compiler can
> handle dynamic signature on the category/domain constructor level.
>
> BforA(P:Cat1, Q: A(P)): Cat2 == B(Q) with { g:%->P }
>
> You can then add the function g without a problem. The moral is: Don't Ask,
> Just
> Tell.
Great! gonna try this!
Martin
- [Axiom-developer] Re: conditionally defined functions, Martin Rubey, 2004/09/17
- [Axiom-developer] Re: conditionally defined functions, Ralf HEMMECKE, 2004/09/17
- [Axiom-developer] Re: conditionally defined functions, Ralf HEMMECKE, 2004/09/17
- [Axiom-developer] Re: conditionally defined functions, William Sit, 2004/09/18
- [Axiom-developer] Re: conditionally defined functions,
Martin Rubey <=
- [Axiom-developer] Re: conditionally defined functions, William Sit, 2004/09/20
- [Axiom-developer] Re: conditionally defined functions, Martin Rubey, 2004/09/22
- [Axiom-developer] Re: conditionally defined functions, William Sit, 2004/09/22
- [Axiom-developer] Re: conditionally defined functions, Martin Rubey, 2004/09/23
- [Axiom-developer] Mixing up variables: (was Re: conditionally defined functions), William Sit, 2004/09/23
- [Axiom-developer] Re: Mixing up variables: (was Re: conditionally defined functions), Martin Rubey, 2004/09/23
- RE: [Axiom-developer] Re: Mixing up variables: (was Re: conditionallydefined functions), Bill Page, 2004/09/23
- RE: [Axiom-developer] Re: Mixing up variables: (was Re: conditionallydefined functions), Martin Rubey, 2004/09/24
- [Axiom-developer] speakerscorner, Martin Rubey, 2004/09/24
- RE: [Axiom-developer] Re: Mixing up variables: (was Re: conditionallydefined functions), Bill Page, 2004/09/24