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Calling Sequence
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nonzero
nonzero(opts)
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Parameters
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opts
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equation(s) of the form option = value where option is one of range, character, or denominator; specify options for the random nonzero rational number
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Description
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The flavor nonzero describes a random nonzero rational number in a particular range.
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To describe a flavor of a random nonzero rational number, use either nonzero or nonzero(opts) (where opts is described following) as the argument to RandomTools[Generate] or as part of a structured flavor.
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By default, the flavor nonzero describes a random nonzero rational number in the range , exclusive, with a denominator that is a factor of .
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You can modify the properties of a random nonzero rational number by using the nonzero(opts) form of this flavor. The opts argument can contain one or more of the following equations.
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This option specifies the range from which the random nonzero rational number is chosen. The left-hand endpoint a is a nonzero rational number and the right-hand endpoint b is a nonzero rational number.
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If the left-hand endpoint of the range is greater than the right-hand endpoint, an exception is raised.
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The default range is .
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character = boundary conditions
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This option specifies whether to include the endpoints of the range from which the random nonzero 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.
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The definitions open and closed are abbreviations for open..open and closed..closed, respectively.
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If the range option is used in conjunction with this option, and a value outside the boundary definition is returned, then the nonzero rational number closest to (but not touching) the range endpoint is chosen.
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This option specifies the positive integer to use as the denominator for the random nonzero rational number that is generated.
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The default denominator for a nonzero flavor is related to . (It depends on whether the endpoints are open or closed and the length of the interval.) The default denominator is .
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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, .
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Examples
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