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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 10:18:38 -0700 (PDT) |
--- Martin Rubey <address@hidden> wrote:
> Currently, you can't. Note that you promise axiom that a1 is a
> Quaternion Fraction Integer. However, you don't hold your promise...
How do I not hold it? I never told it anything about a1 except what
type it is - were did I contradict this?
> What you want is to make a1 a variable. Currently, there is no domain
> of "Variables, which can take values only in Quaternion Fraction
> Integer".
Um. That's surprising, at least to me. (I suppose it wouldn't be if I
understood...) Intuitively I would expect Variable to mean simply "an
unspecified specific instance of a Domain/Type/what have you" with ALL
domains being possible - just so long as you specify the type of the
variable, e.g.:
a1 : Variable(Matrix Quaternion Fraction Integer)
A specific example might be with working in dimensional types: If I
define F as type Force, m as type Mass, and a as type Length/Time^2 I
want to be able to define m1 as type Mass and enter the expression
m*a/m1 into the interperter to return a of type Length/Time^2 without
having to ever specify any particular mass or acceleration. But I want
that type information to be carried and used in the calculations - in
fact, it is essential.
> In fact, it is (or should be) a FAQ. See MathAction.
I took a look at the FAQ link, but I might have missed it. I'll check
again.
> The point of Axioms type system is that any identifier has a typed
> value. There is no such thing as a identifier that does not have a
> value.
>
> If you type
>
> 5*a+a^2
>
> into the interpreter, it responds with
>
> Polynomial Integer.
But what if I want a to have a specific type, for example limit it to
Quaternions only?
> When you say p:=5*a+3*a^2, the identifier p refers to this
> polynomial. The internal representation is something like
>
> [[5,a,1],[3,a,2]]
>
> How would you represent a generic polynomial? You need a different
> domain for that.
I guess I'm not following why things can't be further restricted by
saying in this particulary case a is of type FOO, and therefore doing
two things:
1) restricting the evaluation of the polynomial substitutions for a
which are of type FOO
2) allowing algorithms to use the knowledge that for this polynomial a
is restricted to some subset to make further deductions,
simplifications, and otherwise provide more precise answers
Sorry if this is an obviously trivial question.
Cheers,
CY
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- [Axiom-developer] Question concerning types..., C Y, 2006/09/16
- Re: [Axiom-developer] Question concerning types..., Martin Rubey, 2006/09/16
- Re: [Axiom-developer] Question concerning types...,
C Y <=
- Re: [Axiom-developer] Question concerning types..., Ralf Hemmecke, 2006/09/16
- Re: [Axiom-developer] Question concerning types..., Gabriel Dos Reis, 2006/09/16
- Re: [Axiom-developer] Question concerning types..., C Y, 2006/09/16
- Re: [Axiom-developer] Question concerning types..., Martin Rubey, 2006/09/16
- Re: [Axiom-developer] Question concerning types..., Ralf Hemmecke, 2006/09/16
- Re: [Axiom-developer] Question concerning types..., Gabriel Dos Reis, 2006/09/16
- Re: [Axiom-developer] Question concerning types..., Gabriel Dos Reis, 2006/09/16
- Re: [Axiom-developer] Question concerning types..., C Y, 2006/09/16
- Re: [Axiom-developer] Question concerning types..., Gabriel Dos Reis, 2006/09/16
- Re: [Axiom-developer] Question concerning types..., C Y, 2006/09/16