Algebraic to RPN

[Han]

The code below takes an algebraic expression and converts it to an RPN string. The program itself is not all that useful (in my opinion) but it hopefully provides to those interested in programming expressions a bit of insight into how expressions are built.

For example, in the CAS view, type:

CRPN(x^2-4*x)

to obtain "x 2 ^ 4 x * - +"

EDIT: Joe Horn pointed out to me that the "+" appeared extraneous -- which was also my initial reaction. As it turns out, the CAS treats subtraction as a sequence of negation followed by addition. So the "-" operator is actually the negation operator, which can be verified by typing f:=neg(x) in the CAS view, and extracting the operation using f[1]. I never really gave this much thought, but it is neat to see how expressions are handled on a lower level.

Code:

#pragma mode( separator(.,;) integer(h32) )
#cas
CRPN(f):=
begin
  local rpn, op, par, n, j, g;

  rpn:="";
  op:="";
  par:="";
  if (type(f) <> DOM_SYMBOLIC) then
    rpn:=string(f);
    return(rpn);
  end;

  op:=string(f[1]);
  n:=size(op);
  op:=MID(op,2,n-2);
  n:=dim(f) + 1;

  for j from 2 to n do
    g:=f[j];
    if (type(g) <> DOM_SYMBOLIC) then
      par:=string(g);
    else
      par:=CRPN(g);
    end;
    if (j > 2) then rpn:=rpn + " "; end;
    rpn:=rpn + par;
    if ((j > 2) or (n == 2)) then
      rpn:=rpn + " " + op;
    end;
  end;

  return(rpn);
end;
#end