Built-in Mathematica Symbol

PossibleZeroQ

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

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.

Test whether a numeric expression is zero:

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

Test whether a numeric expression is zero:

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

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:

For arbitrary complex x, f is not identically zero:

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

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 probably correct:

Solving polynomial equations requires deciding whether coefficients are zero:

Mathematica equation solvers use zero testing automatically:

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:

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