rational, rationalize [Function]

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.

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