### The Maxima on-line user's manual

Algebra Calculator

#### Zeroequiv

Function: zeroequiv (<expr>, <v>) Tests whether the expression <expr> in the variable <v> is equivalent to zero, returning `true`, `false`, or `dontknow`.

`zeroequiv` has these restrictions: 1. Do not use functions that Maxima does not know how to differentiate and evaluate.

2. If the expression has poles on the real line, there may be errors in the result (but this is unlikely to occur).

3. If the expression contains functions which are not solutions to first order differential equations (e.g. Bessel functions) there may be incorrect results.

4. The algorithm uses evaluation at randomly chosen points for carefully selected subexpressions. This is always a somewhat hazardous business, although the algorithm tries to minimize the potential for error.

For example `zeroequiv (sin(2*x) - 2*sin(x)*cos(x), x)` returns

`     `true` and `zeroequiv (%e^x + x, x)` returns `false`.  On the`
`     other hand `zeroequiv (log(a*b) - log(a) - log(b), a)` returns`
`     `dontknow` because of the presence of an extra parameter `b`.`

```(%o1)                                true
(%i2) ```

? zeroequiv;

Calculate

? zeroequiv;

Calculate