PossibleZeroQ
✖
PossibleZeroQ
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
open allclose allBasic Examples (1)Summary of the most common use cases
Scope (4)Survey of the scope of standard use cases
Show that a numeric expression is zero:

https://wolfram.com/xid/0fq5vxd0in9hf-bo45up

Show that a numeric expression is nonzero:

https://wolfram.com/xid/0fq5vxd0in9hf-fa8g

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

https://wolfram.com/xid/0fq5vxd0in9hf-b67jz5

Test whether symbolic expressions are likely to be identically zero:

https://wolfram.com/xid/0fq5vxd0in9hf-ccki0f


https://wolfram.com/xid/0fq5vxd0in9hf-kzav8p

Options (2)Common values & functionality for each option
Assumptions (1)
For arbitrary complex x, f is not identically zero:

https://wolfram.com/xid/0fq5vxd0in9hf-cz44s7

https://wolfram.com/xid/0fq5vxd0in9hf-p0zhe

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

https://wolfram.com/xid/0fq5vxd0in9hf-bmot7

Method (1)
By default, numeric approximations may be used to decide that an algebraic number is zero:

https://wolfram.com/xid/0fq5vxd0in9hf-cpl2uk


https://wolfram.com/xid/0fq5vxd0in9hf-krxj0


Approximate methods may give incorrect positive answers:

https://wolfram.com/xid/0fq5vxd0in9hf-mmbp1


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

https://wolfram.com/xid/0fq5vxd0in9hf-cfgmpj

For explicit algebraic numbers the answer is provably correct:

https://wolfram.com/xid/0fq5vxd0in9hf-3gs39

Applications (1)Sample problems that can be solved with this function
Solving polynomial equations requires deciding whether coefficients are zero:

https://wolfram.com/xid/0fq5vxd0in9hf-cl0r7n

https://wolfram.com/xid/0fq5vxd0in9hf-b4vgie

Wolfram Language equation solvers use zero testing automatically:

https://wolfram.com/xid/0fq5vxd0in9hf-3wmqi

Properties & Relations (1)Properties of the function, and connections to other functions
SameQ[e,0] returns True only if e is explicitly identical to zero:

https://wolfram.com/xid/0fq5vxd0in9hf-dw9rbz

https://wolfram.com/xid/0fq5vxd0in9hf-iuc22y

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

https://wolfram.com/xid/0fq5vxd0in9hf-mejslc

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

https://wolfram.com/xid/0fq5vxd0in9hf-cqz8u1

https://wolfram.com/xid/0fq5vxd0in9hf-iaklik

PossibleZeroQ uses numeric methods to test whether ee is zero:

https://wolfram.com/xid/0fq5vxd0in9hf-c7a3un


FullSimplify proves symbolically that ee is zero:

https://wolfram.com/xid/0fq5vxd0in9hf-b7b075

Possible Issues (1)Common pitfalls and unexpected behavior
PossibleZeroQ may return True for nonzero numeric expressions that are close to zero:

https://wolfram.com/xid/0fq5vxd0in9hf-glizhn


https://wolfram.com/xid/0fq5vxd0in9hf-bvl2yq



https://wolfram.com/xid/0fq5vxd0in9hf-ob89ws

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.
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.
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
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: 07-May-2025
]}
BibLaTeX
@online{reference.wolfram_2025_possiblezeroq, organization={Wolfram Research}, title={PossibleZeroQ}, year={2007}, url={https://reference.wolfram.com/language/ref/PossibleZeroQ.html}, note=[Accessed: 07-May-2025
]}