Add license to examples

[linpy.git] / doc / domain.rst

diff --git a/doc/domain.rst b/doc/domain.rst
index 7f99617..06eec6e 100644 (file)
--- a/doc/domain.rst
+++ b/doc/domain.rst
@@ -1,153 +1,180 @@
 Domains Module
 ==============
 
 Domains Module
 ==============
 

+This module provides classes and functions to deal with polyhedral
+domains, i.e. unions of polyhedra.
+

 .. py:class :: Domain
 
 .. py:class :: Domain
 

-    The properties of a domain can be are found using the following 
+    This class represents polyhedral domains, i.e. unions of polyhedra.

 
 

-    .. py:method:: symbols
+    .. py:method:: __new__(cls, *polyhedra)

     
     

-        Returns a tuple of the symbols that exsist in a domain.
+       Create and return a new domain from a string or a list of polyhedra. 

 
 

-    .. py:method:: dimension
+    .. attribute:: polyhedra
+    
+       The tuple of polyhedra which constitute the domain. 

     
     

+    .. attribute:: symbols
+
+        Returns a tuple of the symbols that exsist in a domain.
+
+    .. attribute:: dimension
+

         Returns the number of variables that exist in a domain.
 
         Returns the number of variables that exist in a domain.
 

-    .. py:method:: disjoint
-    
-        Returns a domain as disjoint.
-        
-    .. py:method:: involvesvars(self, vars)
-    
-       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)
     .. py:method:: isempty(self)

-    
+

         Return ``True`` is a domain is empty.
         
         Return ``True`` is a domain is empty.
         

-    .. py:method:: isuniverse(self)
+    .. py:method:: __bool__(self)

     
     

+        Return ``True`` if the domain is non-empty.
+
+    .. py:method:: isuniverse(self)
+

         Return ``True`` if a domain is the Universe set.
         Return ``True`` if a domain is the Universe set.

-                
+

     .. py:method:: isbounded(self)
     .. py:method:: isbounded(self)

-    
-        Return ``True`` if a domain is bounded. 

 
 

-    .. py:method:: disjoint(self)
-    
-        It is not guarenteed that a domain is disjoint. If it is necessary, this method will return a domain as disjoint.
+        Return ``True`` if a domain is bounded.

 
 

-    The following methods compare two domains to find the binary properties.
+    .. py:method:: make_disjoint(self)
+
+        It is not guarenteed that a domain is disjoint. If it is necessary, this method will return an equivalent domain, whose polyhedra are disjoint.

 
     .. py:method:: isdisjoint(self, other)
 
     .. py:method:: isdisjoint(self, other)

-    
+

         Return ``True`` if the intersection of *self* and *other* results in an empty set.
         Return ``True`` if the intersection of *self* and *other* results in an empty set.

-        
+

     .. py:method:: issubset(self, other)
     .. py:method:: issubset(self, other)

-    
+

         Test whether every element in a domain is in *other*.
 
     .. py:method:: __eq__(self, other)
                    self == other
         Test whether every element in a domain is in *other*.
 
     .. py:method:: __eq__(self, other)
                    self == other

-                   
-        Test whether a domain is equal to *other*.  
-        
+
+        Test whether a domain is equal to *other*.
+

     .. py:method:: __lt__(self, other)
                    self < other
     .. py:method:: __lt__(self, other)
                    self < other

-                   
-        Test whether a domain is a strict subset of *other*. 
-        
+
+        Test whether a domain is a strict subset of *other*.
+

     .. py:method:: __le__(self, other)
                    self <= other
     .. py:method:: __le__(self, other)
                    self <= other

-                   
-        Test whether every element in a domain is in *other*.  
-         
+
+        Test whether every element in a domain is in *other*.
+

     .. py:method:: __gt__(self, other)
                    self > other
     .. py:method:: __gt__(self, other)
                    self > other

-                   
-        Test whether a domain is a strict superset of *other*. 
-                
+
+        Test whether a domain is a strict superset of *other*.
+

     .. py:method:: __ge__(self, other)
                    self >= other
     .. py:method:: __ge__(self, other)
                    self >= other

-    
-       Test whether every element in *other* is in a domain.
-        

 
 

-    The following methods implement unary operations on a domain. 
+       Test whether every element in *other* is in a domain.

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

-                   ¬self
+                   ~self
+
+        Return the complementary domain of a domain.
+        
+    .. py:method:: coalesce(self)

     
     

-        Return the complement of a domain.       
+       Simplify the representation of the domain by trying to combine pairs of
+        polyhedra into a single polyhedron. 
+        

         
         

+    .. py:method:: detect_equalities(self)
+    
+        Simplify the representation of the domain by detecting implicit
+        equalities.
+

     .. py:method:: simplify(self)
 
         Return a new domain without any redundant constraints.
 
     .. py:method:: simplify(self)
 
         Return a new domain without any redundant constraints.
 

-    .. py:method:: project(self, dims)
-    
-        Return a new domain with the given dimensions removed.
+    .. py:method:: project(self, variables)
+
+        Return a new domain with the given variables removed.

 
     .. py:method:: aspolyhedron(self)
 
     .. py:method:: aspolyhedron(self)

-    
-        Return polyhedral hull of a domain.        
-        
+
+        Return polyhedral hull of a domain.
+

     .. py:method:: sample(self)
     .. py:method:: sample(self)

-    
-        Return a single sample subset of a domain.

 
 

-    The following methods implement binary operations on two domains. 
+        Return a single sample subset of a domain.

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

+                  __or__

                    self | other
                    self | other

-    
-        Return a new domain with the elements that are common between *self* and *other*.         
+
+        Return a new domain with the elements that are common between *self* and *other*.

 
     .. py:method:: union(self, other)
 
     .. py:method:: union(self, other)

+                  __and__

                    self & other
                    self & other

-    
-        Return a new domain with all the elements from *self* and *other*.   
-            
+
+        Return a new domain with all the elements from *self* and *other*.
+

     .. py:method:: difference(self, other)
     .. py:method:: difference(self, other)

+                  __sub__

                    self - other
                    self - other

-    
-        Return a new domain with the elements in a domain that are not in *other* .     
-              
+
+        Return a new domain with the elements in a domain that are not in *other* .
+

     .. py:method:: __add__(self, other)
                    self + other
     .. py:method:: __add__(self, other)
                    self + other

-    
-        Return the sum of two domains. 
-   
-    The following methods use lexicographical ordering to find the maximum or minimum element in a domain.
+
+        Return the sum of two domains.

 
     .. py:method:: lexmin(self)
 
     .. py:method:: lexmin(self)

-    
-        Return a new set containing the lexicographic minimum of the elements in the set. 
-        
+
+        Return a new domain containing the lexicographic minimum of the elements in the domain.
+

     .. py:method:: lexmax(self)
     .. py:method:: lexmax(self)

+
+        Return a new domain containing the lexicographic maximum of the elements in the domain.
+
+    .. py:method:: subs(self, symbol, expression=None):
+
+        Subsitute symbol by expression in equations and return the resulting
+        domain.
+
+    .. py:method:: fromstring(cls, string)
+        
+        Convert a string into a domain.
+        
+    .. py:method:: fromsympy(cls, expr)

     
     

-        Return a new set containing the lexicographic maximum of the elements in the set.       
+        Convert a SymPy expression into a domain.

         
         

+    .. py:method:: tosympy(self)
+    
+        Convert a domain into a SymPy expression.

 
 

-    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` method. The points, vertices, and faces of a domain can be inspected using the following functions.

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

+
+        Return a list of the points with integer coordinates contained in a domain as :class:`Points` objects.
+        
+    .. py:method:: __contains__(self, point)

     
     

-        Return a list of the points contained in a domain as :class:`Points` objects.
+       Return ``True`` if point if contained within the domain. 

 
     .. py:method:: vertices(self)
 
     .. py:method:: vertices(self)

-    
+

         Return a list of the verticies of a domain.
         Return a list of the verticies of a domain.

-        
+

     .. py:method:: faces(self)
     .. py:method:: faces(self)

-    
+

         Return a list of the vertices for each face of a domain.
         Return a list of the vertices for each face of a domain.

-        
+

     .. py:method:: plot(self, plot=None, **kwargs)
     .. py:method:: plot(self, plot=None, **kwargs)

-    
-        Return a plot of the given domain.       
-        
-          
-        
+
+        Return a plot of the given domain or add a plot to a plot instance, using matplotlib.