WOLFRAM

represents the domain of strictly positive rational numbers, as in xPositiveRationals.

Details

  • xPositiveRationals evaluates immediately if x is a numeric quantity.
  • Simplify[exprPositiveRationals,assum] can be used to try to determine whether an expression corresponds to a positive rational number under the given assumptions.
  • (x1|x2|)PositiveRationals and {x1,x2,}PositiveRationals test whether all xi are positive rational numbers.
  • The domain of positive integers is taken to be a subset of the domain of positive rationals.
  • PositiveRationals is output in StandardForm or TraditionalForm as TemplateBox[{}, PositiveRationals]. This typeset form can be input using prats.

Examples

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Basic Examples  (3)Summary of the most common use cases

2/3 is a positive rational number:

Out[1]=1

A sum of positive rational numbers is a positive rational number:

Out[1]=1

Find positive rational solutions of an equation:

Out[1]=1

Scope  (5)Survey of the scope of standard use cases

Test domain membership of a numeric expression:

Out[1]=1
Out[2]=2
Out[3]=3

Make domain membership assumptions:

Out[1]=1

Specify the default domain over which Reduce should work:

Out[1]=1

Test whether several numbers are positive rationals:

Out[1]=1

If any number is explicitly not a positive rational, the result is False:

Out[2]=2

TraditionalForm formatting:

Properties & Relations  (4)Properties of the function, and connections to other functions

Membership in PositiveRationals is equivalent to membership in Rationals along with positivity:

Out[1]=1

PositiveRationals contains PositiveIntegers:

Out[1]=1

PositiveRationals is contained in PositiveReals, Algebraics and Complexes:

Out[1]=1
Out[2]=2
Out[3]=3

PositiveRationals is disjoint from NonPositiveRationals and NegativeRationals:

Out[1]=1
Out[2]=2
Wolfram Research (2019), PositiveRationals, Wolfram Language function, https://reference.wolfram.com/language/ref/PositiveRationals.html.
Wolfram Research (2019), PositiveRationals, Wolfram Language function, https://reference.wolfram.com/language/ref/PositiveRationals.html.

Text

Wolfram Research (2019), PositiveRationals, Wolfram Language function, https://reference.wolfram.com/language/ref/PositiveRationals.html.

Wolfram Research (2019), PositiveRationals, Wolfram Language function, https://reference.wolfram.com/language/ref/PositiveRationals.html.

CMS

Wolfram Language. 2019. "PositiveRationals." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/PositiveRationals.html.

Wolfram Language. 2019. "PositiveRationals." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/PositiveRationals.html.

APA

Wolfram Language. (2019). PositiveRationals. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PositiveRationals.html

Wolfram Language. (2019). PositiveRationals. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PositiveRationals.html

BibTeX

@misc{reference.wolfram_2024_positiverationals, author="Wolfram Research", title="{PositiveRationals}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/PositiveRationals.html}", note=[Accessed: 10-January-2025 ]}

@misc{reference.wolfram_2024_positiverationals, author="Wolfram Research", title="{PositiveRationals}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/PositiveRationals.html}", note=[Accessed: 10-January-2025 ]}

BibLaTeX

@online{reference.wolfram_2024_positiverationals, organization={Wolfram Research}, title={PositiveRationals}, year={2019}, url={https://reference.wolfram.com/language/ref/PositiveRationals.html}, note=[Accessed: 10-January-2025 ]}

@online{reference.wolfram_2024_positiverationals, organization={Wolfram Research}, title={PositiveRationals}, year={2019}, url={https://reference.wolfram.com/language/ref/PositiveRationals.html}, note=[Accessed: 10-January-2025 ]}