PolynomialQ
PolynomialQ[expr,var]
yields True if expr is a polynomial in var, and yields False otherwise.
PolynomialQ[expr,{var1,…}]
tests whether expr is a polynomial in the vari.
Details
- The vari need not be symbols; PolynomialQ[f[a]+f[a]^2,f[a]] -> True.
Examples
open all close allBasic Examples (2)
Test whether an expression is a polynomial in the specified variable:
PolynomialQ[x ^ 3 - 2x / y + 3x z, x]PolynomialQ[x ^ 3 - 2x / y + 3x z, y]Test whether an expression is a polynomial in the specified set of variables:
PolynomialQ[x ^ 2 + a x y ^ 2 - b Sin[c], {x, y}]PolynomialQ[x ^ 2 + a x y ^ 2 - b Sin[c], {a, b, c}]Properties & Relations (2)
PolynomialQ attempts to find algebraic dependencies between expressions:
PolynomialQ[Sec[x] + 1, Cos[x]]PolynomialQ[x ^ (3 / 2) + 1, Sqrt[x]]PolynomialQ[x ^ (3 / 5) + 1, Sqrt[x]]PolynomialExpressionQ is purely structural and disallows arithmetic expression variables:
PolynomialExpressionQ[Sec[x] + 1, Cos[x]]PolynomialExpressionQ[x ^ (3 / 2) + 1, Sqrt[x]]
Use NonCommutativePolynomialQ to test whether an expression is a noncommutative polynomial:
NonCommutativePolynomialQ[(x + 2y)**(3w**z + 4z**z), {x, y, z, w}]Text
Wolfram Research (1988), PolynomialQ, Wolfram Language function, https://reference.wolfram.com/language/ref/PolynomialQ.html.
CMS
Wolfram Language. 1988. "PolynomialQ." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/PolynomialQ.html.
APA
Wolfram Language. (1988). PolynomialQ. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PolynomialQ.html