Re: Axiom programs which include functions?

"Alasdair McAndrew" <[email protected]> writes:

> 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?

I don't think there is anything that could go wrong.  You can specify an
anonymous function for example with

x +-> x^2-3*x+1

panAxiom doesn't like to do type inference on anonymous functions too much, so
the code will often be interpreted, if you do not specify types:

(1) -> bisect(f, a, b, eps) == (output [a,b]; if abs(fa := f a) < eps then a else if abs(fb := f b) < eps then b else if sign fa = sign fb then error "same sign" else if abs(fz := f(z := ((a+b)/2))) < eps then z else if sign fz = sign fa then bisect(f, z, b, eps) else bisect(f, a, z, eps))
                                                                   Type: Void
(2) -> (x +-> x^2-3*x+1) bisect(x +-> x^2-3*x+1, -2, 0.5, 0.05)

   
   FriCAS will attempt to step through and interpret the code.
   [- 2.0,0.5]
   [- 0.75,0.5]
   [- 0.125,0.5]
   [0.1875,0.5]
   [0.34375,0.5]
   [0.34375,0.421875]

   (2)  - 0.0018920898 4375
                                                                  Type: Float


Does this help?

Martin