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

[Ralf Hemmecke]

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