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.