PossibleZeroQ

PossibleZeroQ(expr)

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

See

• Wikipedia - Constant problem

Examples

Test whether a numeric expression is zero:

>> PossibleZeroQ(E^(I*Pi/4)-(-1)^(1/4))
True

The determination is approximate.

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

>> PossibleZeroQ((x + 1) (x - 1) - x^2 + 1)
True

>> PossibleZeroQ(1/x + 1/y - (x + y)/(x y))
True

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

>> PossibleZeroQ(2^(2*I) - 2^(-2*I) - 2*I*Sin(Log(4)))
True

>> PossibleZeroQ((E + Pi)^2 - E^2 - Pi^2 - 2*E*Pi)
True

>> PossibleZeroQ(Sqrt(x^2) - x)
False

Implementation status

• ✅ - full supported

Github

• Implementation of PossibleZeroQ