Re: Axiom programs which include functions?

Thanks, yes that's what I thought.  There was another subtle error which was
causing my confusion, which I've fixed.

Thanks again,
Alasdair

On Tue, May 20, 2008 at 1:10 AM, Ralf Hemmecke <[email protected]> wrote:

> Hi Alasdair,
>
>
> On 05/19/2008 04:39 PM, Alasdair McAndrew wrote:
>
>> Hi,
>>
>> I can write (simple) Axiom programs for which the parameters are all
>> numbers, but what if the parameters include a function?  Suppose I wished to
>> write a program to, say, solve the equation f(x)=0 by the bisection method,
>> and I wanted to call it as
>>
>> bisect(f,a,b)
>>
>> where [a,b] brackets a solution.  How do I do this?  And in what form does
>> Axiom like its functions in such a program?
>>
>
> A function in Axiom is not so much different from a number. Just do the
> obvious.
>
>
> Suppose you write a function of type
>
> bisect(f: Float -> Float, a: Float, b: Float): Record(result: Float, eps:
> Float) ==
>  ...
>
> where the record stores an approximate result together with an error.
>
> ---BEGIN aaa.spad
> )abbrev domain AAA Aaa
> Aaa: with
>    bisect: (Float -> Float, Float, Float) -> Record(x: Float, eps: Float)
>  == add
>    bisect(f: Float -> Float, a: Float, b: Float): Record(x: Float, eps:
> Float) ==
>        -- insert your bisection algorithm here
>        r: Record(x: Float, eps: Float) := [f a, b-a]
> --------------------------------------------^
> -- This is an example of the application of the input parameter f.
> ---END aaa.spad
>
> Then go to axiom and say:
>
> )co aaa.spad
>
> bisect(sin, 1.0, 2.0)
> bisect(cos, 1.0, 2.0)
>
> Does that help?
>
> Ralf
>

_______________________________________________
Axiom-mail mailing list
[email protected]
http://lists.nongnu.org/mailman/listinfo/axiom-mail