I just wonder if there is difference equations support(package) in maxima

-----maxima-bounces at math.utexas.edu wrote: -----

> Can?I?define?my?own?function?which?has?different?number?of parameters?

Yes, this is possible. The documentation is under ":=" (not so easy to
find):

  "When the last or only function argument x_n is a list of one element,
  the function defined by := accepts a variable number of
  arguments. Actual arguments are assigned one-to-one to formal
  arguments x_1, ..., x_(n - 1), and any further actual arguments, if
  present, are assigned to x_n as a list."

Example:

(%i27) diff_rec2(exp,i, [n]) := (
 n : if n = [] then 1 else first(n),
 if integerp(n) and n > -1 then (
   while n > 0 do (
     exp : sublis([i = i + 1], exp) - exp,
     n : n - 1),
   exp)
else funmake('diff_rec2, [exp,i,n]))$

 (%i29) diff_rec2(f(x),x,1);
 (%o29) f(x+1)-f(x)

 (%i30) diff_rec2(f(x),x,2);
 (%o30) f(x+2)-2*f(x+1)+f(x)

Maybe the function should check that the length of n is 0 or 1:

 (%i31) diff_rec2(f(x),x,2,a,b,c);
 (%o31) f(x+2)-2*f(x+1)+f(x)

Barton