A recursive GCD in CAS - Printable Version +- HP Forums (https://www.hpmuseum.org/forum) +-- Forum: HP Calculators (and very old HP Computers) (/forum-3.html) +--- Forum: HP Prime (/forum-5.html) +--- Thread: A recursive GCD in CAS (/thread-765.html) A recursive GCD in CAS - massimo - 02-25-2014 03:19 AM 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). RE: A recursive GCD in CAS - Mic - 02-25-2014 07:42 PM Very interesting.