**Function:**
inequalities - plot regions defined by inequalities

**Calling Sequence: **

**inequalities( ineqs, xvar = a .. b, yvar = c .. d, options )**

**Parameters: **

**ineqs**
- one inequality or equation or a set of inequalities and equations

**xvar**
- name for the x axis variable

**a, b**
- bounds for
**xvar**
(real constants)

**yvar**
- name for the y axis variable

**c, d **
- bounds for
**yvar**
(real constants)

**options**
- (optional) see below

**Description:**

This is similar to
**inequal**
in the
**plots**
package, but allows nonlinear inequalities and equations.

The plot consists of four elements:

feasible region - the region where all inequalities are satisfied

excluded region - the region where at least one inequality is violated

open lines - curves representing the boundaries of strict (
**<**
) inequalities

closed lines - curves representing the boundaries of non-strict (
**<=**
) inequalities, as well as equations.

Use the options
**optionsfeasible = (...)**
,
**optionsexcluded = (...)**
,
**optionsopen = (...)**
,
**optionsclosed = (...)**
to control the appearance of each of these elements. The defaults are
**optionsfeasible = (colour = green)**
,
**optionsexcluded = (colour = white)**
,
**optionsopen = (colour = red, linestyle=2)**
,
**optionsclosed = (colour = blue, linestyle = 0)**
.

Non-Cartesian coordinates are supported, using the
**coords**
option.

Other two-dimensional plotting options can be used.

This function is part of the Maple Advisor Database library, and must be loaded before use by the command
**readlib(inequalities);**

`> `
**readlib(inequalities):**

`> `
**inequalities({x+y>0, x^2 + y^2 <=3}, x=-2..2, y=-2..2 );**

`> `
**inequalities({x+y>0, x^2-y^2<=1, y=2}, x=-3..3, y=-3..3,
optionsfeasible=(color=cyan),
optionsopen=(color=blue, thickness=2),
optionsclosed=(color=red, thickness=3),
optionsexcluded=(color=aquamarine) );**

`> `
**inequalities(r^2 >= cos(2*theta), r = 0 .. 1.5, theta = 0 .. 2*Pi, coords=polar, labels = [``,``],axes=box);**

**See also:**

__coords__
,
__inequal__
,
__plot(options)__

**Maple Advisor Database **
R. Israel 1998