MuPAD Pro Computing Essentials - Examples 

Example 9.3 - Continued Fractions

Here is the procedure to calculate the coefficients of a continued fraction for the two given numbers n and m, with a finite number of steps.

contFract := proc(n:Type::PosInt,
             m:Type::PosInt,
             steps:Type::PosInt)

local list, i, result, remainder;
begin
   list:=[];
   i:=1;
   while i < steps do
      i:=i+1;
      result:=(n div m);
      remainder:=(n mod m);
      list:=list.[result];
      if remainder<>0 and i<steps then
         n:= m;
         m:= remainder;
      else
         return(list)
      end;
   end;
end:
 

contFract(41319,3340,10)

[12, 2, 1, 2, 3, 2, 26, 2]

Now, we can check if we got the right result.

numlib::contfrac(41319/3340)

12 + 1/(2 + 1/(1 + 1/(2 + 1/(3 + 1/(2 + 1/(26 + 1/
   (2 + 1/...)))))))