rational, rationalize (Function)

Syntax:

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.