# PossibleZeroQ

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.

# 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_2024_possiblezeroq, author="Wolfram Research", title="{PossibleZeroQ}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/PossibleZeroQ.html}", note=[Accessed: 18-September-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_possiblezeroq, organization={Wolfram Research}, title={PossibleZeroQ}, year={2007}, url={https://reference.wolfram.com/language/ref/PossibleZeroQ.html}, note=[Accessed: 18-September-2024 ]}