PolynomialExpressionQ

PolynomialExpressionQ[expr,x]

gives True if expr is structurally a polynomial expression in x, and False otherwise.

PolynomialExpressionQ[expr,{x,y,…}]

gives True if expr is structurally a polynomial expression in x,y,…, and False otherwise.

PolynomialExpressionQ[expr,{x,y,…},test]

gives True if expr is structurally a polynomial expression in x,y,… with coefficients satisfying test, and False otherwise.

Details

  • 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.

Examples

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Basic Examples  (3)

Test whether an expression is a polynomial in the specified variable:

Test whether an expression is a polynomial in the specified set of variables:

Test whether an expression is a polynomial with numeric coefficients:

Scope  (4)

Polynomial expressions may be partially factored:

Coefficients of polynomial expressions may involve arbitrary functions:

Variables need not be symbols:

Variables need not be independent of each other:

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.

Text

Wolfram Research (2020), PolynomialExpressionQ, Wolfram Language function, https://reference.wolfram.com/language/ref/PolynomialExpressionQ.html.

CMS

Wolfram Language. 2020. "PolynomialExpressionQ." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/PolynomialExpressionQ.html.

APA

Wolfram Language. (2020). PolynomialExpressionQ. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PolynomialExpressionQ.html

BibTeX

@misc{reference.wolfram_2024_polynomialexpressionq, author="Wolfram Research", title="{PolynomialExpressionQ}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/PolynomialExpressionQ.html}", note=[Accessed: 22-December-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_polynomialexpressionq, organization={Wolfram Research}, title={PolynomialExpressionQ}, year={2020}, url={https://reference.wolfram.com/language/ref/PolynomialExpressionQ.html}, note=[Accessed: 22-December-2024 ]}