(User.programs)
Item: 211 by _tasmith at hpcvbbs.UUCP
Author: [Ted A Smith]
  Subj: Rational number package
  Date: Wed Feb 06 1991 20:21 

[Note: On this disk, RATPAC is a directory object, and RATPAC.LIB is a library
object.  They have the same functionality.  -jkh-]

Here is a rational math package:

  QAdd  Add two numbers
  QSub  Subtract
  QMul  Multiply
  QDiv  Divide
  QNeg  Negate
  QInv  Reciprocate
  Q->I  Convert a number to an integer
  Q->F  Convert a number to a continued fraction
  QF->  Convert a continued fraction to a number
  ->NUM Convert a number to a real

CST will be a menu.

Input numbers may be real or rationals.
Rationals are represented as 'i+n/d' or 'n/d', e.g.
  5 2 QDiv        ==>  '5/2'
  '5/2' 2 QAdd    ==>  '4+1/2'

I took reasonable care to preserve high accuracy.
I don't have a clue what possesed me to write this.
There isn't near enough error checking on input expressions.

P.S. By truncating a continued fraction you can get the 'best'
approximation to your input number with a denominator <= the
resultant denominator.  E.g.
  'Pi' ->NUM                   ==>  3.14159265359
  3.14159265359 Q->F           ==>  { 3 7 15 1 292 1 1 3 }
  { 3 7 15 1 292 1 1 3 } QF->  ==>  3.14159265359
  { 3 7 15 1 } QF->            ==>  '355/113'
  { 3 7 } QF->                 ==>  '22/7'

[Note: By decrementing (not dropping) the last number in the list, you reduce
 the resulting fraction by the smallest possible amount.  This fact is what
 makes the DEC2FRAC program work.  Number theory buffs will enjoy taking
 successive results from DEC2FRAC and feeding them to Ted's Q->F function.
 -jkh-]