Update docs

[linpy.git] / doc / examples.rst

diff --git a/doc/examples.rst b/doc/examples.rst
index a4b0f5a..62a7dfd 100644 (file)
--- a/doc/examples.rst
+++ b/doc/examples.rst
@@ -1,9 +1,9 @@
 LinPy Examples
 ==============
 
-Creating a Polyhedron
------------------
-    To create any polyhedron, first define the symbols used. Then use the polyhedron functions to define the constraints for the polyhedron. This example creates a square.
+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 *
     >>> x, y = symbols('x y')
@@ -11,25 +11,37 @@ Creating a Polyhedron
     >>> square1 = Le(0, x) & Le(x, 2) & Le(0, y) & Le(y, 2)
     >>> print(square1)
     And(Ge(x, 0), Ge(-x + 2, 0), Ge(y, 0), Ge(-y + 2, 0))
-
-Urnary Operations
------------------
-
+    
+    Binary operations and properties examples:
+    
+    >>> square2 = Le(2, x) & Le(x, 4) & Le(2, y) & Le(y, 4)
+    >>> #test equality 
+    >>> square1 == square2
+    False
+    >>> # find the union of two polygons 
+    >>> square1 + square2
+    Or(And(Ge(x, 0), Ge(-x + 2, 0), Ge(y, 0), Ge(-y + 2, 0)), And(Ge(x - 2, 0), Ge(-x + 4, 0), Ge(y - 2, 0), Ge(-y + 4, 0)))
+    >>> # check if square1 and square2 are disjoint
+    >>> square1.disjoint(square2)
+    False
+    >>> # find the intersection of two polygons
+    >>> square1 & square2
+    And(Eq(y - 2, 0), Eq(x - 2, 0))
+    >>> # find the convex union of two polygons
+    >>> Polyhedron(square1 | sqaure2)
+    And(Ge(x, 0), Ge(-x + 4, 0), Ge(y, 0), Ge(-y + 4, 0), Ge(x - y + 2, 0), Ge(-x + y + 2, 0))
+    
+    Unary operation and properties examples:
+    
     >>> square1.isempty()
     False
-    >>> square1.isbounded()
-    True
-
-Binary Operations
------------------
-
-     >>> square2 = Le(2, x) & Le(x, 4) & Le(2, y) & Le(y, 4)
-     >>> square1 + square2
-     Or(And(Ge(x, 0), Ge(-x + 2, 0), Ge(y, 0), Ge(-y + 2, 0)), And(Ge(x - 2, 0), Ge(-x + 4, 0), Ge(y - 2, 0), Ge(-y + 4, 0)))
-     >>> # check if square1 and square2 are disjoint
-     >>> square1.disjoint(square2)
-     False
-
+    >>> square1.symbols()
+    (x, y)
+    >>> square1.inequalities
+    (x, -x + 2, y, -y + 2)
+    >>> square1.project([x])
+    And(Ge(-y + 2, 0), Ge(y, 0))
+    
 Plot Examples
 -------------
 
@@ -51,7 +63,7 @@ Plot Examples
      .. figure:: images/cube.jpg
         :align:  center
 
-     The user can also inspect a polygon's vertices and the integer points included in the polygon.
+     LinPy can also inspect a polygon's vertices and the integer points included in the polygon.
 
      >>> diamond = Ge(y, x - 1) & Le(y, x + 1) & Ge(y, -x - 1) & Le(y, -x + 1)
      >>> diamond.vertices()
@@ -59,9 +71,3 @@ Plot Examples
      >>> 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})]
 
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