RationalExpressionQ
RationalExpressionQ[expr,x]
gives True if expr is structurally a rational expression in x, and False otherwise.
RationalExpressionQ[expr,{x,y,…}]
gives True if expr is structurally a rational expression in x,y,…, and False otherwise.
RationalExpressionQ[expr,{x,y,…},test]
gives True if expr is structurally a rational expression in x,y,… with coefficients satisfying test, and False otherwise.
Details
- A rational expression in x,y,… is an expression constructed with x,y,… and coefficients not containing x,y,…, using Plus, Times and integer Power.
- RationalExpressionQ[expr,vars,NumericQ] tests whether expr is a rational expression in vars with numeric coefficients.
Examples
open all close allBasic Examples (3)
Scope (4)
Properties & Relations (2)
Together represents rational expressions as ratios of polynomials:
Use NumeratorDenominator to extract the numerator and the denominator:
Use PolynomialExpressionQ to verify that the resulting expressions are polynomials:
Rational expressions represent functions that are singular at zeros of the denominators:
Use FunctionSingularities to find the singularities:
Outside zeros of the denominators, rational expressions represent analytic functions:
Possible Issues (3)
A rational expression may not represent a rational function due to hidden division by zero:
A nonrational expression may represent a rational function:
RationalExpressionQ is purely syntactic:
Syntactically, Tan[x] is a coefficient, free of Sin[x] and Cos[x]:
Text
Wolfram Research (2020), RationalExpressionQ, Wolfram Language function, https://reference.wolfram.com/language/ref/RationalExpressionQ.html.
CMS
Wolfram Language. 2020. "RationalExpressionQ." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/RationalExpressionQ.html.
APA
Wolfram Language. (2020). RationalExpressionQ. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RationalExpressionQ.html