The flavor rational describes a random rational number in a particular range.

To describe a flavor of a random rational number, use either rational or rational(opts) (where opts is described following) as the argument to RandomTools[Generate] or as part of a structured flavor.

By default, the flavor rational describes a random rational number in the range , inclusive, with a denominator that is a factor of .

You can modify the properties of a random rational number by using the rational(opts) form of this flavor. The opts argument can contain one or more of the following equations.

range = a..b

This option describes the range from which the random rational number is chosen. The endpoints must be of type rational and they describe a random rational number in the interval . The inclusiveness of a and b are determined by the character option.

If the left-hand endpoint of the range is greater than the right-hand endpoint, an exception is raised.

character = boundary definition

This option specifies whether to include the endpoints of the range from which the random rational number is chosen. Six boundary definitions are valid: open, closed, open..open, open..closed, closed..open, and closed..closed. The default value for this option is open.

The definitions open and closed are abbreviations for open..open and closed..closed, respectively.

denominator = posint

This option specifies the positive integer to use as the denominator for the random rational number that is generated.

The default denominator for a rational flavor is related to . (It depends on whether the endpoints are open or closed and the length of the interval.) The default denominator is .

In the case of the closed interval , the denominator has only  factors (, , , ) only two of which are under . Therefore, a result of  cannot occur. Instead, you can specify a denominator that is highly composite. For example, .