[Axiom-mail] Function inside a function?

[Alasdair McAndrew]

I have been experimenting with writing a few little programs to perform numerical integration, in which I have been running into difficulties.  I can do all the operations I need from the command line, but I run into problems when I try to bundle those commands into a program.

As a simple example, suppose I wanted a program to implement the two-point Gaussian rule, which approximates the integral of f(x) between -1 and 1 by f(-1/sqrt(3))+f(1/sqrt(3)).

On an interval other than [-1,1], we need a scaling transformation.  So I might have a file called "gauss2.input" which contains one function:

gauss2(f,a,b)==
  xs:LIST Float := [-1/sqrt(3),1/sqrt(3)]
  g := (x:Float):Float +-> f((b-a)/2*x+(b+a)/2)
  int2 := (b-a)/2*(g(xs.1) + g(xs.2))
  return(int2)

However, the system clams up on the use of the scaling function g(x), and this gives no results.

I have two questions here: first, how do I get round this?  and second, if I'm writing programs, should I be writing them in Aldor (that's the language of ".input" files, isn't it?), or SPAD?

For that matter, how do all the languages Aldor, SPAD, Lisp, Boot link up - which is used for which purpose, and why?

Thanks,

Alasdair

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