gives True if expr is structurally a polynomial expression in x, and False otherwise.
gives True if expr is structurally a polynomial expression in x,y,…, and False otherwise.
gives True if expr is structurally a polynomial expression in x,y,… with coefficients satisfying test, and False otherwise.
- A polynomial expression in x,y,… is an expression constructed with x,y,…, and coefficients not containing x,y,…, using Plus, Times and positive integer Power.
- PolynomialExpressionQ[expr,vars,NumericQ] tests whether expr is a polynomial expression in vars with numeric coefficients.
Examplesopen allclose all
Basic Examples (3)
Properties & Relations (5)
Expand represents polynomial expressions as sums of monomials:
Factor represents polynomial expressions as products of irreducible factors:
The factors are polynomial expressions:
A ratio of polynomial expressions is a rational expression:
Use RationalExpressionQ to test that the fraction is a rational expression:
Polynomial expressions represent analytic functions:
Use FunctionAnalytic to verify that f is analytic:
PolynomialQ attempts to find algebraic dependencies between expressions:
PolynomialExpressionQ is purely structural and disallows arithmetic expression variables:
Possible Issues (2)
A non-polynomial expression may represent a polynomial function:
PolynomialExpressionQ is purely syntactic:
Syntactically, Sin[x] is a coefficient, free of Cos[x] and Tan[x]:
Wolfram Research (2020), PolynomialExpressionQ, Wolfram Language function, https://reference.wolfram.com/language/ref/PolynomialExpressionQ.html.
Wolfram Language. 2020. "PolynomialExpressionQ." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/PolynomialExpressionQ.html.
Wolfram Language. (2020). PolynomialExpressionQ. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PolynomialExpressionQ.html