**Error:**
division by zero

In mathematics, division by zero is not allowed. In Maple, an attempt to divide by zero produces this error.

`> `
**sin(0)/0;**

Error, division by zero

In some cases when a division by zero results from evaluating some expression at a certain value of a variable
, what is really wanted instead is the limit of the expression as
approaches this value. This may be obtained by using
**limit**
.

`> `
**limit(sin(x)/x, x=0);**

Sometimes a division by zero can result when Maple fails to recognize early enough that some quantity is 0.

`> `
**series(p/((1-sin(x-p)^2 - cos(x+p)^2)), p = 0,3);**

`> `
**simplify(");**

Error, (in simplify/trig) division by zero

When this occurs in
**series**
and related commands, you may be able to fix the problem by changing the environment variable Testzero, whose value is the procedure used in
**series**
to determine when the leading coefficient is 0. By default this just uses
**normal**
.

`> `
**eval(Testzero);**

You can replace
**normal**
by
**simplify**
to get a stronger test.

`> `
**Testzero:= proc(O) evalb(simplify(O)=0) end:**

Since
**series**
has the
**remember**
option, if you try the same
**series**
command again it will just remember the value it computed before. To get it to try again, you can make it forget the past values.

`> `
**readlib(forget)(series);**

`> `
**series(p/((1-sin(x-p)^2 - cos(x+p)^2)), p = 0,3);**

There is also a bug in Release 4 that causes this error to occur in some integrals involving products of half-integer powers of linear terms.

`> `
**int((2*x+1)^(-3/2)*x^(1/2),x=0..1);**

Error, (in int) division by zero

A work-around is to express the integrand as a single square root.

`> `
**F:= int(((2*x+1)^(-3)*x)^(1/2),x=0..1);**

**See also:**
__forget__
,
__int__
,
Integrals involving fractional powers
,
__limit__
,
__normal__
,
__series__
,
__simplify__
,
__Testzero__

**Maple Advisor Database**
R. Israel, 1998