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NegativeRationals
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NegativeRationals

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represents the domain of strictly negative rational numbers, as in x∈NegativeRationals.

Details

  • x∈NegativeRationals evaluates immediately if x is a numeric quantity.
  • Simplify[expr∈NegativeRationals,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

open allclose all

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

-2/3 is a negative rational number:

In[1]:=1
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https://wolfram.com/xid/01zdhb9onag-s1074
Out[1]=1

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

In[1]:=1
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https://wolfram.com/xid/01zdhb9onag-l7nnc
Out[1]=1

Find negative rational solutions of an equation:

In[1]:=1
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https://wolfram.com/xid/01zdhb9onag-bemtf7
Out[1]=1

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

Test domain membership of a numeric expression:

In[1]:=1
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https://wolfram.com/xid/01zdhb9onag-crra11
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/01zdhb9onag-f8i88p
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/01zdhb9onag-i6yxp8
Out[3]=3

Make domain membership assumptions:

In[1]:=1
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https://wolfram.com/xid/01zdhb9onag-cn7igo
Out[1]=1

Specify the default domain over which Reduce should work:

In[1]:=1
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https://wolfram.com/xid/01zdhb9onag-g9ic3l
Out[1]=1

Test whether several numbers are negative rationals:

In[1]:=1
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https://wolfram.com/xid/01zdhb9onag-3pjyzh
Out[1]=1

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

In[2]:=2
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https://wolfram.com/xid/01zdhb9onag-m7ag79
Out[2]=2

TraditionalForm formatting:

In[1]:=1
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https://wolfram.com/xid/01zdhb9onag-4xdcq9

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

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

In[1]:=1
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https://wolfram.com/xid/01zdhb9onag-bus6sg
Out[1]=1

NegativeRationals contains NegativeIntegers:

In[1]:=1
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https://wolfram.com/xid/01zdhb9onag-bpv7ri
Out[1]=1

NegativeRationals is contained in NegativeReals, Algebraics and Complexes:

In[1]:=1
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https://wolfram.com/xid/01zdhb9onag-culh0e
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/01zdhb9onag-i9rm0h
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/01zdhb9onag-oij108
Out[3]=3

NegativeRationals is disjoint from NonNegativeRationals and PositiveRationals:

In[1]:=1
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https://wolfram.com/xid/01zdhb9onag-3ius3z
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/01zdhb9onag-pe30t4
Out[2]=2
Wolfram Research (2019), NegativeRationals, Wolfram Language function, https://reference.wolfram.com/language/ref/NegativeRationals.html.
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Wolfram Research (2019), NegativeRationals, Wolfram Language function, https://reference.wolfram.com/language/ref/NegativeRationals.html.

Text

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

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

CMS

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

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

APA

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

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

BibTeX

@misc{reference.wolfram_2025_negativerationals, author="Wolfram Research", title="{NegativeRationals}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/NegativeRationals.html}", note=[Accessed: 12-May-2025 ]}

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@misc{reference.wolfram_2025_negativerationals, author="Wolfram Research", title="{NegativeRationals}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/NegativeRationals.html}", note=[Accessed: 12-May-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_negativerationals, organization={Wolfram Research}, title={NegativeRationals}, year={2019}, url={https://reference.wolfram.com/language/ref/NegativeRationals.html}, note=[Accessed: 12-May-2025 ]}

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@online{reference.wolfram_2025_negativerationals, organization={Wolfram Research}, title={NegativeRationals}, year={2019}, url={https://reference.wolfram.com/language/ref/NegativeRationals.html}, note=[Accessed: 12-May-2025 ]}