A recursive GCD in CAS

[massimo]

CAS is a sort of functional language like LISP or F#. Functional languages often uses recursion in place of loops. Combining recursive and piecewise functions give us all the necessary tools to write powerful "CAS programs" without using HP-PPL.
To test these concepts I wrote a GCD function:

\[
mgcdr(z,w):=z-w*IP(z/w)
\]
\[
mgcdi(z,w) :=
\begin{cases}
{w \ \mbox{if} \ mgcdr(z,w)=0}
\\
{mgcdi(w,mgcdr(z,w)) \ \mbox{if} \ mgcdr(z,w) \neq 0}
\end{cases}
\]
\[
mgcd(a,b):=mgcdi(MAX(|a|,|b|),MIN(|a|,|b|))
\]

Or in HP Prime syntax:

Code:


mgcdr(z,w):=z-w*IP((z/w))
mgcdi(z,w):=PIECEWISE((mgcdr(z,w)) = 0,w,(mgcdr(z,w))≠0,mgcdi(w,mgcdr(z,w)))
mgcd(a,b):=mgcdi(MAX(ABS(a),ABS(b)),MIN(ABS(a),ABS(b)))

Note that combining functions is often convenient.
Sure it is less efficient than an HP-PPL equivalent program:

Code:


EXPORT MCD(n,d)
BEGIN
 LOCAL z,w,t;
 z:=MAX(ABS(n),ABS(d));
 w:=MIN(ABS(n),ABS(d));
 WHILE w≠0 DO
  t:=z;
  z:=w;
  w:=t-w*IP(t/w);
 END;
 RETURN z;
END;

but I find this approach very interesting (especially when you need to manage lists).