PossibleZeroQ—Wolfram Documentation

PossibleZeroQ[expr]

gives True if basic symbolic and numerical methods suggest that expr has value zero, and gives False otherwise.

Details and Options

The general problem of determining whether an expression has value zero is undecidable; PossibleZeroQ provides a quick but not always accurate test.
With the setting Method->"ExactAlgebraics", PossibleZeroQ will use exact guaranteed methods in the case of explicit algebraic numbers.
PossibleZeroQ takes the following options:
Assumptions $Assumptions assumptions on parameters

Method Automatic method to use

Examples

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Basic Examples (1)

Test whether a numeric expression is zero:

Test whether a symbolic expression is likely to be identically zero:

Scope (4)

Show that a numeric expression is zero:

Show that a numeric expression is nonzero:

Decide that a numeric expression is zero based on approximate computations:

Test whether symbolic expressions are likely to be identically zero:

Options (2)

Assumptions (1)

For arbitrary complex x, f is not identically zero:

When Re[x]>0, f is identically zero:

Method (1)

By default, numeric approximations may be used to decide that an algebraic number is zero:

Approximate methods may give incorrect positive answers:

With Method->"ExactAlgebraics" exact methods are used for explicit algebraic numbers:

For explicit algebraic numbers the answer is provably correct:

Applications (1)

Solving polynomial equations requires deciding whether coefficients are zero:

Wolfram Language equation solvers use zero testing automatically:

Properties & Relations (1)

SameQ[e,0] returns True only if e is explicitly identical to zero:

Equal[e,0] uses simple tests to decide whether e is zero:

When Equal cannot decide whether an expression is zero it returns unchanged:

PossibleZeroQ uses numeric methods to test whether ee is zero:

FullSimplify proves symbolically that ee is zero:

Possible Issues (1)

PossibleZeroQ may return True for nonzero numeric expressions that are close to zero:

Wolfram Research (2007), PossibleZeroQ, Wolfram Language function, https://reference.wolfram.com/language/ref/PossibleZeroQ.html.

Text

Wolfram Research (2007), PossibleZeroQ, Wolfram Language function, https://reference.wolfram.com/language/ref/PossibleZeroQ.html.

CMS

Wolfram Language. 2007. "PossibleZeroQ." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/PossibleZeroQ.html.

APA

Wolfram Language. (2007). PossibleZeroQ. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PossibleZeroQ.html

BibTeX

@misc{reference.wolfram_2025_possiblezeroq, author="Wolfram Research", title="{PossibleZeroQ}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/PossibleZeroQ.html}", note=[Accessed: 22-February-2026]}

BibLaTeX

@online{reference.wolfram_2025_possiblezeroq, organization={Wolfram Research}, title={PossibleZeroQ}, year={2007}, url={https://reference.wolfram.com/language/ref/PossibleZeroQ.html}, note=[Accessed: 22-February-2026]}

	Assumptions	$Assumptions	assumptions on parameters
	Method	Automatic	method to use