rational, rationalize
rational, rationalize Function
Syntax:
rational number → rational
rationalize number → rational
Arguments and Values:
number—a real.
rational—a rational.
Description:
rational and rationalize convert reals to rationals.
If number is already rational, it is returned.
If number is a float, rational returns a rational that is mathematically equal in value to the float. rationalize returns a rational that approximates the float to the accuracy of the underlying floating-point representation.
rational assumes that the float is completely accurate.
rationalize assumes that the float is accurate only to the precision of the floating-point representation.
Examples:
(rational 0) → 0
(rationalize -11/100) → -11/100
(rational .1) → 13421773/134217728 ;implementation-dependent
(rationalize .1) → 1/10
Affected By:
The implementation.
Exceptional Situations:
Should signal an error of type type-error if number is not a real. Might signal arithmetic-error.
Notes:
It is always the case that
(float (rational x) x) ≡ x
and
(float (rationalize x) x) ≡ x
That is, rationalizing a float by either method and then converting it back to a float of the same format produces the original number.
Expanded Reference: rational, rationalize
TODO: Please contribute to this page by adding explanations and examples
(rational, rationalize )