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7.4.8 Rationalize

(require 'rationalize)

— Function: rationalize x e

Computes the correct result for exact arguments (provided the implementation supports exact rational numbers of unlimited precision); and produces a reasonable answer for inexact arguments when inexact arithmetic is implemented using floating-point.

Rationalize has limited use in implementations lacking exact (non-integer) rational numbers. The following procedures return a list of the numerator and denominator.

— Function: find-ratio x e

find-ratio returns the list of the simplest numerator and denominator whose quotient differs from x by no more than e. 

(find-ratio 3/97 .0001)             ⇒ (3 97)
     (find-ratio 3/97 .001)              ⇒ (1 32)
— Function: find-ratio-between x y

find-ratio-between returns the list of the simplest numerator and denominator between x and y. 

(find-ratio-between 2/7 3/5)        ⇒ (1 2)
     (find-ratio-between -3/5 -2/7)      ⇒ (-1 2)