NegativeRationals

NegativeRationals

represents the domain of strictly negative rational numbers, as in xNegativeRationals.

Details

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

Examples

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Basic Examples  (3)

-2/3 is a negative rational number:

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

Find negative rational solutions of an equation:

Scope  (5)

Test domain membership of a numeric expression:

Make domain membership assumptions:

Specify the default domain over which Reduce should work:

Test whether several numbers are negative rationals:

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

TraditionalForm formatting:

Properties & Relations  (4)

Membership in NegativeRationals is equivalent to membership in Rationals and negativity:

NegativeRationals contains NegativeIntegers:

NegativeRationals is contained in NegativeReals, Algebraics and Complexes:

NegativeRationals is disjoint from NonNegativeRationals and PositiveRationals:

Introduced in 2019
 (12.0)