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:

NumeratorDenominator automatically threads over lists:

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.

BibTeX

@misc{reference.wolfram_2021_numeratordenominator, author="Wolfram Research", title="{NumeratorDenominator}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/NumeratorDenominator.html}", note=[Accessed: 12-June-2021 ]}

BibLaTeX

@online{reference.wolfram_2021_numeratordenominator, organization={Wolfram Research}, title={NumeratorDenominator}, year={2019}, url={https://reference.wolfram.com/language/ref/NumeratorDenominator.html}, note=[Accessed: 12-June-2021 ]}

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