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  (2)

Extract the numerator and denominator of a rational number:

Extract the numerator and denominator of a rational expression:

Scope  (5)

Rational numbers:

Gaussian rationals:

Rational expressions:

Select terms with syntactically positive and negative exponents:

Reconstruct the original expression:

NumeratorDenominator automatically threads over lists:

Options  (2)

Modulus  (1)

Find numerators and denominators over integers modulo :

Trig  (1)

Numerators and denominators of trigonometric functions:

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:

Introduced in 2019
 (12.0)