A hidden zero is a quantity that is identically equal to zero but for which it is nontrivial to construct a proof of equality.
Hidden zeros can be problematic for computer algebra systems. For example, failing to detect a hidden zero in a denominator can lead to symbolic expressions that are invalid because they contain division by 0.
In the Wolfram Language, simple hidden zeroes such as
 |
(1)
|
 |
(2)
|
do not automatically evaluate to 0, but functions such as Simplify and FunctionExpandcan reduce them to 0. For more complicated expressions such as
 |
(3)
|
 |
(4)
|
 |
(5)
|
FullSimplify can be used (sometimes in combination with TrigToExp).
More complicated hidden zeros such as
 |
(6)
|
where 
is a hypergeometric
function and 
is a gamma function, can require specialized simplifiers
or heuristic methods such as PossibleZeroQ
in the Wolfram Language.
