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 $\mathrm{-1}..1$, 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 $\mathrm{-1}..1$, the denominator has only $4$ factors ($2$, $11$, $124847$, $182041$) only two of which are under $100000$. Therefore, a result of $\frac{1}{3}$ cannot occur. Instead, you can specify a denominator that is highly composite. For example, $720720$.

$\mathrm{with}\left(\mathrm{RandomTools}\right)\:$

$\mathrm{Generate}\left(\mathrm{rational}\right)$

$-\frac{104281139459}{499999999994}$

$\mathrm{Generate}\left(\mathrm{rational}\left(\mathrm{range}=-2..5\right)\right)$

$\frac{1112405903299}{249999999997}$

$\mathrm{Generate}\left(\mathrm{rational}\left(\mathrm{range}=-5..\frac{1}{2}\,\mathrm{denominator}=720720\right)\right)$

$-\frac{691783}{144144}$

$\mathrm{Generate}\left(\mathrm{rational}\left(\mathrm{denominator}=10\right)\right)$

$-\frac{2}{5}$

$\mathrm{sort}\left(\left[\mathrm{seq}\left(\mathrm{Generate}\left(\mathrm{rational}\left(\mathrm{denominator}=6\,\mathrm{character}=\mathrm{open}..\mathrm{closed}\right)\right)\,i=1..10\right)\right]\,'\mathrm{numeric}'\right)$

$\left[-\frac{5}{6}\,-\frac{2}{3}\,-\frac{1}{3}\,-\frac{1}{6}\,-\frac{1}{6}\,0\,\frac{1}{3}\,\frac{5}{6}\,\frac{5}{6}\,1\right]$

$\mathrm{Generate}\left(\mathrm{list}\left(\mathrm{rational}\left(\mathrm{range}=\frac{7}{2}..\frac{13}{2}\right)\,10\right)\right)$

$\left[\frac{1617959967603}{249999999997}\,\frac{2444607189245}{499999999994}\,\frac{2523012980003}{499999999994}\,\frac{1240308146463}{249999999997}\,\frac{1856507053637}{499999999994}\,\frac{2146412722983}{499999999994}\,\frac{89133474041}{22727272727}\,\frac{227279279289}{45454545454}\,\frac{1589678109779}{249999999997}\,\frac{107533275874}{22727272727}\right]$

$\mathrm{seq}\left(\mathrm{Generate}\left(\mathrm{rational}\left(\mathrm{range}=0..7\,\mathrm{denominator}=720720\right)\right)\,i=1..10\right)$

$\frac{4238413}{720720},\frac{857911}{360360},\frac{1074583}{180180},\frac{430957}{240240},\frac{886631}{360360},\frac{579803}{102960},\frac{91609}{102960},\frac{913459}{720720},\frac{39779}{180180},\frac{972275}{144144}$

$\mathrm{Matrix}\left(3\,3\,\mathrm{Generate}\left(\mathrm{rational}\left(\mathrm{denominator}=24\right)\mathrm{identical}\left(x\right)+\mathrm{rational}\left(\mathrm{denominator}=16\right)\,\mathrm{makeproc}=\mathrm{true}\right)\right)$

$\left[\begin{array}{ccc}\frac{2x}{3}+\frac{5}{8}& -\frac{7x}{8}+\frac{1}{16}& -\frac{7x}{8}-\frac{11}{16}\\ \frac{13x}{24}-\frac{3}{8}& \frac{x}{12}-\frac{3}{8}& \frac{x}{8}-\frac{7}{8}\\ -\frac{2x}{3}+\frac{1}{4}& \frac{23x}{24}-\frac{7}{8}& -\frac{5x}{8}+\frac{5}{16}\end{array}\right]$