Re: [Axiom-mail] Axiom programs which include functions?

[Alasdair McAndrew]

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 <address@hidden> 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