how to define the composition of functions

You'll find suggestions in the Maxima mailing list; search 
"compose functions" in 

   http://maxima.sourceforge.net/maximalist.html

To define "o" to be an infix composition function, use infix("o").
Try something like

(%i14) infix("o")$

Taken from to_poly_solver.mac:

(%i17) compose_functions(l) := block([z : ?gensym(), f],
  if listp(l) then (
    l : reverse(l),
    f : z,
    for lk in l do f : funmake(lk, [f]),
    buildq([z,f], lambda([z], f)))
  else error("The argument to 'compose_functions' must be a list."))$

(%i19) "o"(p,q) := compose_functions([p,q])$

(%i20) p o q;
(%o20) lambda([g33538],p(q(g33538)))

Ouch! Maxima doesn't know the function algebra:

(%i22) f : p o q - q o p;
(%o22) lambda([g33541],p(q(g33541)))-lambda([g33542],q(p(g33542)))


(%i23) f(x);
f evaluates to lambda([g33541],p(q(g33541)))-lambda([g33542],q(p(g33542)))
Improper name or value in functional position.

Barton

maxima-bounces at math.utexas.edu wrote on 05/05/2009 08:58:20 AM:

> [image removed] 
> 
> [Maxima] how to define the composition of functions
> 
> Kursat Aker 
> 
> to:
> 
> maxima
> 
> 05/05/2009 08:59 AM
> 
> Sent by:
> 
> maxima-bounces at math.utexas.edu
> 
> 
> Hello,
> 
> I would like to know how one can define the composition of functionsin 
maxima.
> Say,
> p( psi ) := diff( psi, x);
> q( psi ) := x*psi;
> How can I define a composition operator, say o ?
> I would like to define the lie bracket on the space one-variable 
functions.
> Thanks,
> kursat
> 
> 
> 
> 
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