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PolynomialQ

Polynomial (SymPy, WMA)

PolynomialQ[expr]

returns True if expr is a polynomial and returns False otherwise.

PolynomialQ[expr, var]

returns True if expr is a polynomial in var, and returns False otherwise.

PolynomialQ[expr, {var1, ...}]

tests whether expr is a polynomial in the vari.

PolynomialQ with no explicit variable mentioned:

• • PolynomialQ[x^2]

A number is a degenerate kind of polynomial:

• • PolynomialQ[2]

The following is not a polynomial because y is raised to the power -1:

• • PolynomialQ[x^2 + x/y]

PolynomialQ using an expression and a single variable:

• • PolynomialQ[x^3 - 2 x/y + 3xz, x]

In the above, there were no negative powers for x. In the below when we check with respect to y, we do find y is raised to a negative power:

• • PolynomialQ[x^3 - 2 x/y^2 + 3xz, y]

• • PolynomialQ[f[a] + f[a]^2, f[a]]

  • $$\mathrm{True}$$

PolynomialQ using an expression and a list of variables:

• • PolynomialQ[x^2 + axy^2 - bSin[c], {x, y}]

  • $$\mathrm{True}$$

• • PolynomialQ[x^2 + axy^2 - bSin[c], {a, b, c}]

  • $$\mathrm{False}$$