RandomTools Flavor: rational
describe a flavor of a random rational number
equation(s) of the form option = value where option is one of range, character, or denominator; specify options for the random rational number
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 −1..1, inclusive, with a denominator that is a factor of 499999999994.
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 a..b. 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 999999999989. (It depends on whether the endpoints are open or closed and the length of the interval.) The default denominator is 499999999994.
In the case of the closed interval −1..1, the denominator has only 4 factors (2, 11, 124847, 182041) only two of which are under 100000. Therefore, a result of 13 cannot occur. Instead, you can specify a denominator that is highly composite. For example, 720720.
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