Remove license and add to doc examples

[linpy.git] / doc / examples.rst

diff --git a/doc/examples.rst b/doc/examples.rst
index 1884f49..3d2626d 100644 (file)
--- a/doc/examples.rst
+++ b/doc/examples.rst
@@ -2,7 +2,8 @@ LinPy Examples
 ==============
 
 Basic Examples
--------------
+--------------
+
     To create any polyhedron, first define the symbols used. Then use the polyhedron functions to define the constraints. The following is a simple running example illustrating some different operations and properties that can be performed by LinPy with two squares.
 
     >>> from linpy import *
@@ -11,16 +12,19 @@ Basic Examples
     >>> square1 = Le(0, x) & Le(x, 2) & Le(0, y) & Le(y, 2)
     >>> square1
     And(Ge(x, 0), Ge(-x + 2, 0), Ge(y, 0), Ge(-y + 2, 0))
-    
+
     Binary operations and properties examples:
-    
-    >>> square2 = Le(1, x) & Le(x, 3) & Le(1, y) & Le(y, 3)
-    >>> #test equality 
+
+    >>> # create a polyhedron from a string
+    >>> square2 = Polyhedron('1 <= x') & Polyhedron('x <= 3') & \
+    Polyhedron('1 <= y') & Polyhedron('y <= 3')
+    >>> #test equality
     >>> square1 == square2
     False
     >>> # compute the union of two polyhedrons
     >>> square1 | square2
-    Or(And(Ge(x, 0), Ge(-x + 2, 0), Ge(y, 0), Ge(-y + 2, 0)), And(Ge(x - 1, 0), Ge(-x + 3, 0), Ge(y - 1, 0), Ge(-y + 3, 0)))
+    Or(And(Ge(x, 0), Ge(-x + 2, 0), Ge(y, 0), Ge(-y + 2, 0)), \
+    And(Ge(x - 1, 0), Ge(-x + 3, 0), Ge(y - 1, 0), Ge(-y + 3, 0)))
     >>> # check if square1 and square2 are disjoint
     >>> square1.disjoint(square2)
     False
@@ -29,12 +33,17 @@ Basic Examples
     And(Ge(x - 1, 0), Ge(-x + 2, 0), Ge(y - 1, 0), Ge(-y + 2, 0))
     >>> # compute the convex union of two polyhedrons
     >>> Polyhedron(square1 | sqaure2)
-    And(Ge(x, 0), Ge(y, 0), Ge(-y + 3, 0), Ge(-x + 3, 0), Ge(x - y + 2, 0), Ge(-x + y + 2, 0))
-    
+    And(Ge(x, 0), Ge(y, 0), Ge(-y + 3, 0), Ge(-x + 3, 0), \
+    Ge(x - y + 2, 0), Ge(-x + y + 2, 0))
+
     Unary operation and properties examples:
-    
+
     >>> square1.isempty()
     False
+    >>> # compute the complement of square1
+    >>> ~square1
+    Or(Ge(-x - 1, 0), Ge(x - 3, 0), And(Ge(x, 0), Ge(-x + 2, 0), \
+    Ge(-y - 1, 0)), And(Ge(x, 0), Ge(-x + 2, 0), Ge(y - 3, 0)))
     >>> square1.symbols()
     (x, y)
     >>> square1.inequalities
@@ -42,7 +51,7 @@ Basic Examples
     >>> # project out the variable x
     >>> square1.project([x])
     And(Ge(-y + 2, 0), Ge(y, 0))
-    
+
 Plot Examples
 -------------
 
@@ -78,9 +87,9 @@ LinPy can also inspect a polygon's vertices and the integer points included in t
      >>> diamond.points()
      [Point({x: -1, y: 0}), Point({x: 0, y: -1}), Point({x: 0, y: 0}), \
      Point({x: 0, y: 1}), Point({x: 1, y: 0})]
-     
+
 The user also can pass another plot to the :meth:`plot` method. This can be useful to compare two polyhedrons on the same axis. This example illustrates the union of two squares.
-     
+
     >>> from linpy import *
     >>> import matplotlib.pyplot as plt
     >>> from matplotlib import pylab
@@ -93,11 +102,11 @@ The user also can pass another plot to the :meth:`plot` method. This can be usef
     >>> square2.plot(plot, facecolor='blue', alpha=0.3)
     >>> squares = Polyhedron(square1 + square2)
     >>> squares.plot(plot, facecolor='blue', alpha=0.3)
-    >>> pylab.show()  
-     
+    >>> pylab.show()
+
     .. figure:: images/union.jpg
-       :align:  center 
-     
-     
-     
+       :align:  center
+
+
+