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@code{(require 'rationalize)}
@ftindex rationalize


@defun 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.

@end defun

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


@defun find-ratio x e

@code{find-ratio} returns the list of the @emph{simplest}
numerator and denominator whose quotient differs from @var{x} by no more
than @var{e}.

@format
@t{(find-ratio 3/97 .0001)             @result{} (3 97)
(find-ratio 3/97 .001)              @result{} (1 32)
}
@end format
@end defun


@defun find-ratio-between x y

@code{find-ratio-between} returns the list of the @emph{simplest}
numerator and denominator between @var{x} and @var{y}.

@format
@t{(find-ratio-between 2/7 3/5)        @result{} (1 2)
(find-ratio-between -3/5 -2/7)      @result{} (-1 2)
}
@end format
@end defun