# NumeratorDenominator

NumeratorDenominator[expr]

gives the list {Numerator[expr],Denominator[expr]} of expr.

# Details and Options

• Numerator picks out terms that do not have superficially negative exponents. Denominator picks out the remaining terms.
• An exponent is "superficially negative" if it has a negative number as a factor.
• The standard representation of rational expressions as products of powers means that you cannot simply use Part to extract numerators.
• NumeratorDenominator can be used on rational numbers.
• NumeratorDenominator automatically threads over lists.

# Examples

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## Basic Examples(3)

Extract the numerator and denominator of a rational number:

Extract the numerator and denominator of a rational expression:

Extract the numerator and denominator of a symbolic expression:

## Scope(7)

Rational numbers:

Gaussian rationals:

Rational expressions:

Select terms with syntactically positive and negative exponents:

Reconstruct the original expression:

Compute the numerator and denominator over the integers modulo 5:

Compute the numerator and denominator while incorporating common trigonometric identities:

## Options(2)

### Modulus(1)

Find numerators and denominators over integers modulo :

### Trig(1)

Numerators and denominators of trigonometric functions:

## Applications(2)

Compute the numerator and denominator with respect to a specified modulus:

Compute the limit at infinity of a rational function:

Extract the numerator and denominator:

Apply Exponent to find the degree of the numerator and denominator:

We can see that the denominator has a larger degree. Thus, the function approaches zero as grows large:

This can be confirmed using Limit:

## Properties & Relations(1)

An expression is a quotient of its numerator and denominator:

## Neat Examples(1)

Plot semitransparent blue squares at positions {i, j} for which i/j is an irreducible fraction:

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

#### Text

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

#### CMS

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

#### APA

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

#### BibTeX

@misc{reference.wolfram_2024_numeratordenominator, author="Wolfram Research", title="{NumeratorDenominator}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/NumeratorDenominator.html}", note=[Accessed: 10-September-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_numeratordenominator, organization={Wolfram Research}, title={NumeratorDenominator}, year={2019}, url={https://reference.wolfram.com/language/ref/NumeratorDenominator.html}, note=[Accessed: 10-September-2024 ]}