Update plot examples

diff --git a/doc/domain.rst b/doc/domain.rst
index 4cd79d9..edf8934 100644 (file)
--- a/doc/domain.rst
+++ b/doc/domain.rst
@@ -3,8 +3,6 @@ Domains Module
 
 .. py:class :: Domain
 
 
 .. py:class :: Domain
 

-    The properties of a domain can be are found using the following
-

     .. py:method:: symbols
 
         Returns a tuple of the symbols that exsist in a domain.
     .. py:method:: symbols
 
         Returns a tuple of the symbols that exsist in a domain.


@@ -21,8 +19,6 @@ Domains Module
 
        Returns ``True`` if a domain depends on the given dimensions.
 
 
        Returns ``True`` if a domain depends on the given dimensions.
 

-    The unary properties of a domain can be inspected using the following methods.
-

     .. py:method:: isempty(self)
 
         Return ``True`` is a domain is empty.
     .. py:method:: isempty(self)
 
         Return ``True`` is a domain is empty.


@@ -39,8 +35,6 @@ Domains Module
 
         It is not guarenteed that a domain is disjoint. If it is necessary, this method will return a domain as disjoint.
 
 
         It is not guarenteed that a domain is disjoint. If it is necessary, this method will return a domain as disjoint.
 

-    The following methods compare two domains to find the binary properties.
-

     .. py:method:: isdisjoint(self, other)
 
         Return ``True`` if the intersection of *self* and *other* results in an empty set.
     .. py:method:: isdisjoint(self, other)
 
         Return ``True`` if the intersection of *self* and *other* results in an empty set.


@@ -74,9 +68,6 @@ Domains Module
 
        Test whether every element in *other* is in a domain.
 
 
        Test whether every element in *other* is in a domain.
 

-
-    The following methods implement unary operations on a domain.
-

     .. py:method:: complement(self)
                    ¬self
 
     .. py:method:: complement(self)
                    ¬self
 


@@ -98,8 +89,6 @@ Domains Module
 
         Return a single sample subset of a domain.
 
 
         Return a single sample subset of a domain.
 

-    The following methods implement binary operations on two domains.
-

     .. py:method:: intersection(self, other)
                    self | other
 
     .. py:method:: intersection(self, other)
                    self | other
 


@@ -120,8 +109,6 @@ Domains Module
 
         Return the sum of two domains.
 
 
         Return the sum of two domains.
 

-    The following methods use lexicographical ordering to find the maximum or minimum element in a domain.
-

     .. py:method:: lexmin(self)
 
         Return a new set containing the lexicographic minimum of the elements in the set.
     .. py:method:: lexmin(self)
 
         Return a new set containing the lexicographic minimum of the elements in the set.


@@ -131,7 +118,7 @@ Domains Module
         Return a new set containing the lexicographic maximum of the elements in the set.
 
 
         Return a new set containing the lexicographic maximum of the elements in the set.
 
 

-    A 2D or 3D domain can be plotted using the :meth:`plot` function. The points, verticies, and faces of a domain can be inspected using the following functions.
+A 2D or 3D domain can be plotted using the :meth:`plot` function. The points, verticies, and faces of a domain can be inspected using the following functions.

 
     .. py:method:: points(self)
 
 
     .. py:method:: points(self)
 

diff --git a/doc/examples.rst b/doc/examples.rst
index 62a7dfd..13c59fc 100644 (file)
--- a/doc/examples.rst
+++ b/doc/examples.rst
@@ -18,16 +18,16 @@ Basic Examples
     >>> #test equality 
     >>> square1 == square2
     False
     >>> #test equality 
     >>> square1 == square2
     False

-    >>> # find the union of two polygons 
-    >>> square1 + square2
+    >>> # compute 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
     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
+    >>> # compute the intersection of two polygons

     >>> square1 & square2
     And(Eq(y - 2, 0), Eq(x - 2, 0))
     >>> square1 & square2
     And(Eq(y - 2, 0), Eq(x - 2, 0))

-    >>> # find the convex union of two polygons
+    >>> # compute 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))
     
     >>> 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))
     


@@ -39,6 +39,7 @@ Basic Examples
     (x, y)
     >>> square1.inequalities
     (x, -x + 2, y, -y + 2)
     (x, y)
     >>> square1.inequalities
     (x, -x + 2, y, -y + 2)

+    >>> # project out the variable x

     >>> square1.project([x])
     And(Ge(-y + 2, 0), Ge(y, 0))
     
     >>> square1.project([x])
     And(Ge(-y + 2, 0), Ge(y, 0))
     


@@ -70,4 +71,26 @@ Plot Examples
      [Point({x: Fraction(0, 1), y: Fraction(1, 1)}), Point({x: Fraction(-1, 1), y: Fraction(0, 1)}), Point({x: Fraction(1, 1), y: Fraction(0, 1)}), Point({x: Fraction(0, 1), y: Fraction(-1, 1)})]
      >>> 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})]
      [Point({x: Fraction(0, 1), y: Fraction(1, 1)}), Point({x: Fraction(-1, 1), y: Fraction(0, 1)}), Point({x: Fraction(1, 1), y: Fraction(0, 1)}), Point({x: Fraction(0, 1), y: Fraction(-1, 1)})]
      >>> 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
+    >>> x, y = symbols('x y')
+    >>> square1 = Le(0, x) & Le(x, 2) & Le(0, y) & Le(y, 2)
+    >>> square2 = Le(1, x) & Le(x, 3) & Le(1, y) & Le(y, 3)
+    >>> fig = plt.figure()
+    >>> plot = fig.add_subplot(1, 1, 1, aspect='equal')
+    >>> square1.plot(plot, facecolor='red', alpha=0.3)
+    >>> square2.plot(plot, facecolor='blue', alpha=0.3)
+    >>> squares = Polyhedron(square1 + square2)
+    >>> squares.plot(plot, facecolor='blue', alpha=0.3)
+    >>> pylab.show()  
+     
+    .. figure:: images/union.jpg
+       :align:  center 
+     
+     
+     

 
 

diff --git a/doc/images/union.jpg b/doc/images/union.jpg
new file mode 100644 (file)
index 0000000..7d14ae8
Binary files /dev/null and b/doc/images/union.jpg differ

diff --git a/doc/linexpr.rst b/doc/linexpr.rst
index 4101252..2aab652 100644 (file)
--- a/doc/linexpr.rst
+++ b/doc/linexpr.rst
@@ -3,6 +3,9 @@ Linear Expression Module
 
 This class implements linear expressions.
 
 
 This class implements linear expressions.
 

+.. py:class:: Expression
+
+

     .. py:method:: coefficient(self, symbol)
         
         Return the coefficient value of the given symbol.
     .. py:method:: coefficient(self, symbol)
         
         Return the coefficient value of the given symbol.


@@ -38,6 +41,9 @@ This class implements linear expressions.
     .. py:method:: tosympy(self)
     
         Return an expression as a sympy object.    
     .. py:method:: tosympy(self)
     
         Return an expression as a sympy object.    

+
+.. py:class:: Symbol(Expression)
+        

           
 .. py:class:: Dummy(Symbol)
 
           
 .. py:class:: Dummy(Symbol)
 

diff --git a/doc/polyhedra.rst b/doc/polyhedra.rst
index 736cff6..47462a7 100644 (file)
--- a/doc/polyhedra.rst
+++ b/doc/polyhedra.rst
@@ -3,7 +3,7 @@ Polyhedra Module
 
 .. py:class:: Polyhedron
 
 
 .. py:class:: Polyhedron
 

-    Polyhedron class allows users to build and inspect polyherons.  The following methods provide the properties of a polyhedron.
+    Polyhedron class allows users to build and inspect polyherons.

 
     .. py:method:: equalities(self)
 
 
     .. py:method:: equalities(self)
 


@@ -17,8 +17,6 @@ Polyhedra Module
 
         Return ta list of the constraints of a polyhedron.
 
 
         Return ta list of the constraints of a polyhedron.
 

-    The following unary operations can be used to inspect a polyhedron.
-

     .. py:method:: disjoint(self)
 
         Returns a polyhedron as a disjoint.
     .. py:method:: disjoint(self)
 
         Returns a polyhedron as a disjoint.