This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.1)

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, 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:
In[1]:=
Click for copyable input
Out[1]=
Test whether a symbolic expression is likely to be identically zero:
In[2]:=
Click for copyable input
Out[2]=
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 , is not identically zero:
When Re[x]>0, 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 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 returns True only if e is explicitly identical to zero:
Equal 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 is zero:
FullSimplify proves symbolically that is zero:
PossibleZeroQ may return True for nonzero numeric expressions that are close to zero:
New in 6