Doc updates (not complete)

diff --git a/doc/domain.rst b/doc/domain.rst
index b85b2d0..06eec6e 100644 (file)
--- a/doc/domain.rst
+++ b/doc/domain.rst
@@ -1,8 +1,21 @@
 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
 

+    This class represents polyhedral domains, i.e. unions of polyhedra.
+
+    .. py:method:: __new__(cls, *polyhedra)
+    
+       Create and return a new domain from a string or a list of polyhedra. 
+
+    .. attribute:: polyhedra
+    
+       The tuple of polyhedra which constitute the domain. 
+    

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


@@ -14,6 +27,10 @@ Domains Module
     .. py:method:: isempty(self)
 
         Return ``True`` is a domain is empty.
     .. py:method:: isempty(self)
 
         Return ``True`` is a domain is empty.

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

 
     .. py:method:: isuniverse(self)
 
 
     .. py:method:: isuniverse(self)
 


@@ -23,9 +40,9 @@ Domains Module
 
         Return ``True`` if a domain is bounded.
 
 
         Return ``True`` if a domain is bounded.
 

-    .. py:method:: disjoint(self)
+    .. py:method:: make_disjoint(self)

 
 

-        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 an equivalent domain, whose polyhedra are disjoint.

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


@@ -63,7 +80,18 @@ Domains Module
     .. py:method:: complement(self)
                    ~self
 
     .. py:method:: complement(self)
                    ~self
 

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


@@ -106,18 +134,38 @@ Domains Module
 
     .. 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 set containing the lexicographic maximum of the elements in the set.
+        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)
+    
+        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` method. The points, vertices, and faces of a domain can be inspected using the following functions.
 
     .. py:method:: points(self)
 
 
 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)
 

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

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


@@ -129,4 +177,4 @@ A 2D or 3D domain can be plotted using the :meth:`plot` method. The points, vert
 
     .. py:method:: plot(self, plot=None, **kwargs)
 
 
     .. py:method:: plot(self, plot=None, **kwargs)
 

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

diff --git a/doc/linexpr.rst b/doc/linexpr.rst
index b5d8069..eb2f704 100644 (file)
--- a/doc/linexpr.rst
+++ b/doc/linexpr.rst
@@ -4,8 +4,11 @@ Linear Expression Module
 This class implements linear expressions. A linear expression is….
 
 .. py:class:: Expression
 This class implements linear expressions. A linear expression is….
 
 .. py:class:: Expression

-
-
+    
+    .. py:method:: __new__(cls, coefficients=None, constant=0)
+        
+        Create and return a new linear expression from a string or a list of coefficients and a constant.
+        

     .. 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.


@@ -26,13 +29,67 @@ This class implements linear expressions. A linear expression is….
     
         Return the number of variables in an expression.
         
     
         Return the number of variables in an expression.
         

+    .. py:method:: isconstant(self)
+        
+        Return ``True`` if an expression is a constant.
+    
+    .. py:method:: issymbol(self)
+    
+        Return ``True`` if an expression is a symbol.       
+    
+        
+    .. py:method:: values(self)
+    
+        Return the coefficient and constant values of an expression.
+        
+    .. py:method:: __add__(self, other)
+    
+        Return the sum of *self* and *other*.
+        

     .. py:method:: __sub__(self, other)
     
         Return the difference between *self* and *other*.
     .. py:method:: __sub__(self, other)
     
         Return the difference between *self* and *other*.

-               
+
+    .. py:method:: __mul__(self, other)
+    
+        Return the product of *self* and *other* if *other* is a rational number.
+    
+    .. py:method:: __eq__(self, other)
+        
+        Test whether two expressions are equal.
+                
+    .. py:method:: __le__(self, other)
+                   self <= other
+
+        Create a new polyhedra from an expression with a single constraint as *self* less than or equal to *other*.    
+
+    .. py:method:: __lt__(self, other)
+                   self < other
+                   
+       Create a new polyhedra from an expression with a single constraint as *self* less than *other*.  
+                                      
+    .. py:method:: __ge__(self, other)
+                   self >= other    
+        
+        Create a new polyhedra from an expression with a single constraint as *self* greater than or equal to *other*.  
+        
+    .. py:method:: __gt__(self, other)
+                   self > other
+        
+        Create a new polyhedra from an expression with a single constraint as *self* greater than *other*.  
+        
+    .. py:method:: scaleint(self)
+    
+        Multiply an expression by a scalar to make all coefficients integer values.
+                                  

     .. py:method:: subs(self, symbol, expression=None)
     
         Subsitute the given value into an expression and return the resulting expression.
     .. py:method:: subs(self, symbol, expression=None)
     
         Subsitute the given value into an expression and return the resulting expression.

+        
+        
+    .. py:method:: fromstring(self)
+    
+        Create an expression from a string.

 
     .. py:method:: fromsympy(self)
     
 
     .. py:method:: fromsympy(self)
     


@@ -43,8 +100,41 @@ This class implements linear expressions. A linear expression is….
         Return an expression as a sympy object.    
 
 .. py:class:: Symbol(Expression)
         Return an expression as a sympy object.    
 
 .. py:class:: Symbol(Expression)

+
+    .. py:method:: __new__(cls, name)
+    
+        Create and return a symbol from a string.
+        
+    .. py:method::  symbols(names)
+    
+        This function returns a sequence of symbols with names taken from names argument, which can be a comma or whitespace delimited string, or a sequence of strings.

         
         

+    .. py:method:: asdummy(self)
+        
+        Return a symbol as a :class:`Dummy` Symbol.

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

-This class returns a dummy symbol to ensure that each no variables are repeated in an expression   
+    This class returns a dummy symbol to ensure that no variables are repeated in an expression. This is useful when the user needs to have a unique symbol, for example as a temporary one in some calculation, which is going to be substituted for something else at the end anyway.    
+    
+    .. py:method:: __new__(cls, name=None)
+        
+        Create and return a new dummy symbol.
+        
+    
+.. py:class:: Rational(Expression, Fraction)
+
+    This class represents integers and rational numbers of any size.
+    
+    .. attribute:: constant
+       
+        Return rational as a constant.
+
+    .. py:method:: isconstant(self)
+        
+        Test whether a value is a constant.
+
+    .. py:method:: fromsympy(cls, expr)
+        
+       Create a rational object from a sympy expression 
+    

diff --git a/doc/modules.rst b/doc/modules.rst
index bf383c7..4859f2d 100644 (file)
--- a/doc/modules.rst
+++ b/doc/modules.rst
@@ -11,7 +11,7 @@ There are four main LinPy modules, all of them can be inherited at once with the
    :maxdepth: 2
 
    linexpr.rst
    :maxdepth: 2
 
    linexpr.rst

-   polyhedra.rst

    domain.rst
    domain.rst

+   polyhedra.rst

    geometry.rst
    
    geometry.rst
    

diff --git a/doc/polyhedra.rst b/doc/polyhedra.rst
index 1f2756b..f6f1a30 100644 (file)
--- a/doc/polyhedra.rst
+++ b/doc/polyhedra.rst
@@ -1,33 +1,51 @@
 Polyhedra Module
 ================
 
 Polyhedra Module
 ================
 

-Polyhedron class allows users to build and inspect polyherons.
+Polyhedron class allows users to build and inspect polyherons. Polyhedron inherits all methods from the :class:`Domain` class.

 
 

-.. py:class:: Polyhedron
+.. py:class:: Polyhedron(Domain)

 
 

-    .. py:property:: equalities
+    .. py:method::  __new__(cls, equalities=None, inequalities=None)
+    
+        Create and return a new Polyhedron from a string or list of equalities and inequalities.
+
+    .. attribute:: equalities

 
         Returns a list of the equalities in a polyhedron.
 
 
         Returns a list of the equalities in a polyhedron.
 

-    .. py:property:: inequalities
+    .. attribute:: inequalities

 
         Returns a list of the inequalities in a polyhedron.
 
 
         Returns a list of the inequalities in a polyhedron.
 

-    .. py:property:: constraints
+    .. attribute:: constraints

 
         Returns a list of the constraints of a polyhedron.
 
 
         Returns a list of the constraints of a polyhedron.
 

-    .. py:method:: disjoint(self)
+    .. py:method:: make_disjoint(self)

 
         Returns a polyhedron as a disjoint.
 
     .. py:method:: isuniverse(self)
 
         Return ``True`` if a polyhedron is the Universe set.
 
         Returns a polyhedron as a disjoint.
 
     .. py:method:: isuniverse(self)
 
         Return ``True`` if a polyhedron is the Universe set.

+        
+    .. py:method:: aspolyhedron(self)
+    
+        Return the polyhedral hull of a polyhedron.    
+
+    .. py:method:: __contains__(self, point)
+
+        Report whether a polyhedron constains an integer point

 
     .. py:method:: subs(self, symbol, expression=None)
 
 
     .. py:method:: subs(self, symbol, expression=None)
 

-        Substitutes an expression into a polyhedron and returns the result.
+        Subsitute the given value into an expression and return the resulting
+        expression.
+
+    .. py:method:: fromstring(cls, string)
+        
+        Create and return a Polyhedron from a string.
+       

 
 To create a polyhedron, the user can use the following functions to define  equalities and inequalities as the constraints.
 
 
 To create a polyhedron, the user can use the following functions to define  equalities and inequalities as the constraints.
 

diff --git a/linpy/linexprs.py b/linpy/linexprs.py
index aedf170..bc36fda 100644 (file)
--- a/linpy/linexprs.py
+++ b/linpy/linexprs.py
@@ -49,6 +49,9 @@ class Expression:
     """
 
     def __new__(cls, coefficients=None, constant=0):
     """
 
     def __new__(cls, coefficients=None, constant=0):

+        """
+        Create a new expression.
+        """

         if isinstance(coefficients, str):
             if constant != 0:
                 raise TypeError('too many arguments')
         if isinstance(coefficients, str):
             if constant != 0:
                 raise TypeError('too many arguments')


@@ -82,6 +85,9 @@ class Expression:
         return self
 
     def coefficient(self, symbol):
         return self
 
     def coefficient(self, symbol):

+        """
+        Return the coefficient value of the given symbol.
+        """

         if not isinstance(symbol, Symbol):
             raise TypeError('symbol must be a Symbol instance')
         return Rational(self._coefficients.get(symbol, 0))
         if not isinstance(symbol, Symbol):
             raise TypeError('symbol must be a Symbol instance')
         return Rational(self._coefficients.get(symbol, 0))


@@ -89,31 +95,52 @@ class Expression:
     __getitem__ = coefficient
 
     def coefficients(self):
     __getitem__ = coefficient
 
     def coefficients(self):

+        """
+        Return a list of the coefficients of an expression
+        """

         for symbol, coefficient in self._coefficients.items():
             yield symbol, Rational(coefficient)
 
     @property
     def constant(self):
         for symbol, coefficient in self._coefficients.items():
             yield symbol, Rational(coefficient)
 
     @property
     def constant(self):

+        """
+        Return the constant value of an expression.
+        """

         return Rational(self._constant)
 
     @property
     def symbols(self):
         return Rational(self._constant)
 
     @property
     def symbols(self):

+        """
+        Return a list of symbols in an expression.
+        """

         return self._symbols
 
     @property
     def dimension(self):
         return self._symbols
 
     @property
     def dimension(self):

+        """
+        Create and return a new linear expression from a string or a list of coefficients and a constant.
+        """

         return self._dimension
 
     def __hash__(self):
         return hash((tuple(self._coefficients.items()), self._constant))
 
     def isconstant(self):
         return self._dimension
 
     def __hash__(self):
         return hash((tuple(self._coefficients.items()), self._constant))
 
     def isconstant(self):

+        """
+        Return true if an expression is a constant.
+        """

         return False
 
     def issymbol(self):
         return False
 
     def issymbol(self):

+        """
+        Return true if an expression is a symbol.
+        """

         return False
 
     def values(self):
         return False
 
     def values(self):

+        """
+        Return the coefficient and constant values of an expression.
+        """

         for coefficient in self._coefficients.values():
             yield Rational(coefficient)
         yield Rational(self._constant)
         for coefficient in self._coefficients.values():
             yield Rational(coefficient)
         yield Rational(self._constant)


@@ -129,6 +156,9 @@ class Expression:
 
     @_polymorphic
     def __add__(self, other):
 
     @_polymorphic
     def __add__(self, other):

+        """
+        Return the sum of two expressions.
+        """

         coefficients = defaultdict(Fraction, self._coefficients)
         for symbol, coefficient in other._coefficients.items():
             coefficients[symbol] += coefficient
         coefficients = defaultdict(Fraction, self._coefficients)
         for symbol, coefficient in other._coefficients.items():
             coefficients[symbol] += coefficient


@@ -139,6 +169,9 @@ class Expression:
 
     @_polymorphic
     def __sub__(self, other):
 
     @_polymorphic
     def __sub__(self, other):

+        """
+        Return the difference between two expressions.
+        """

         coefficients = defaultdict(Fraction, self._coefficients)
         for symbol, coefficient in other._coefficients.items():
             coefficients[symbol] -= coefficient
         coefficients = defaultdict(Fraction, self._coefficients)
         for symbol, coefficient in other._coefficients.items():
             coefficients[symbol] -= coefficient


@@ -150,6 +183,9 @@ class Expression:
         return other - self
 
     def __mul__(self, other):
         return other - self
 
     def __mul__(self, other):

+        """
+        Return the product of two expressions if other is a rational number.
+        """

         if isinstance(other, numbers.Rational):
             coefficients = ((symbol, coefficient * other)
                 for symbol, coefficient in self._coefficients.items())
         if isinstance(other, numbers.Rational):
             coefficients = ((symbol, coefficient * other)
                 for symbol, coefficient in self._coefficients.items())


@@ -169,8 +205,9 @@ class Expression:
 
     @_polymorphic
     def __eq__(self, other):
 
     @_polymorphic
     def __eq__(self, other):

-        # returns a boolean, not a constraint
-        # see http://docs.sympy.org/dev/tutorial/gotchas.html#equals-signs
+        """
+        Test whether two expressions are equal
+        """

         return isinstance(other, Expression) and \
             self._coefficients == other._coefficients and \
             self._constant == other._constant
         return isinstance(other, Expression) and \
             self._coefficients == other._coefficients and \
             self._constant == other._constant


@@ -192,11 +229,18 @@ class Expression:
         return Gt(self, other)
 
     def scaleint(self):
         return Gt(self, other)
 
     def scaleint(self):

+        """
+        Multiply an expression by a scalar to make all coefficients integer values.
+        """

         lcm = functools.reduce(lambda a, b: a*b // gcd(a, b),
             [value.denominator for value in self.values()])
         return self * lcm
 
     def subs(self, symbol, expression=None):
         lcm = functools.reduce(lambda a, b: a*b // gcd(a, b),
             [value.denominator for value in self.values()])
         return self * lcm
 
     def subs(self, symbol, expression=None):

+        """
+        Subsitute symbol by expression in equations and return the resulting
+        expression.
+        """

         if expression is None:
             if isinstance(symbol, Mapping):
                 symbol = symbol.items()
         if expression is None:
             if isinstance(symbol, Mapping):
                 symbol = symbol.items()


@@ -244,6 +288,9 @@ class Expression:
 
     @classmethod
     def fromstring(cls, string):
 
     @classmethod
     def fromstring(cls, string):

+        """
+        Create an expression from a string.
+        """

         # add implicit multiplication operators, e.g. '5x' -> '5*x'
         string = Expression._RE_NUM_VAR.sub(r'\1*\2', string)
         tree = ast.parse(string, 'eval')
         # add implicit multiplication operators, e.g. '5x' -> '5*x'
         string = Expression._RE_NUM_VAR.sub(r'\1*\2', string)
         tree = ast.parse(string, 'eval')


@@ -306,6 +353,9 @@ class Expression:
 
     @classmethod
     def fromsympy(cls, expr):
 
     @classmethod
     def fromsympy(cls, expr):

+        """
+        Convert sympy object to an expression.
+        """

         import sympy
         coefficients = []
         constant = 0
         import sympy
         coefficients = []
         constant = 0


@@ -321,6 +371,9 @@ class Expression:
         return Expression(coefficients, constant)
 
     def tosympy(self):
         return Expression(coefficients, constant)
 
     def tosympy(self):

+        """
+        Return an expression as a sympy object.  
+        """

         import sympy
         expr = 0
         for symbol, coefficient in self.coefficients():
         import sympy
         expr = 0
         for symbol, coefficient in self.coefficients():


@@ -333,6 +386,9 @@ class Expression:
 class Symbol(Expression):
 
     def __new__(cls, name):
 class Symbol(Expression):
 
     def __new__(cls, name):

+        """
+        Create and return a symbol from a string.
+        """

         if not isinstance(name, str):
             raise TypeError('name must be a string')
         self = object().__new__(cls)
         if not isinstance(name, str):
             raise TypeError('name must be a string')
         self = object().__new__(cls)


@@ -360,6 +416,9 @@ class Symbol(Expression):
         return self.sortkey() == other.sortkey()
 
     def asdummy(self):
         return self.sortkey() == other.sortkey()
 
     def asdummy(self):

+        """
+        Return a symbol as a Dummy Symbol.
+        """

         return Dummy(self.name)
 
     @classmethod
         return Dummy(self.name)
 
     @classmethod


@@ -390,10 +449,15 @@ class Symbol(Expression):
 
 
 class Dummy(Symbol):
 
 
 class Dummy(Symbol):

-
+    """
+    This class returns a dummy symbol to ensure that no variables are repeated in an expression
+    """

     _count = 0
 
     def __new__(cls, name=None):
     _count = 0
 
     def __new__(cls, name=None):

+        """
+        Create and return a new dummy symbol.
+        """

         if name is None:
             name = 'Dummy_{}'.format(Dummy._count)
         elif not isinstance(name, str):
         if name is None:
             name = 'Dummy_{}'.format(Dummy._count)
         elif not isinstance(name, str):


@@ -422,12 +486,18 @@ class Dummy(Symbol):
 
 
 def symbols(names):
 
 
 def symbols(names):

+    """
+    Transform strings into instances of the Symbol class
+    """

     if isinstance(names, str):
         names = names.replace(',', ' ').split()
     return tuple(Symbol(name) for name in names)
 
 
 class Rational(Expression, Fraction):
     if isinstance(names, str):
         names = names.replace(',', ' ').split()
     return tuple(Symbol(name) for name in names)
 
 
 class Rational(Expression, Fraction):

+    """
+    This class represents integers and rational numbers of any size.
+    """

 
     def __new__(cls, numerator=0, denominator=None):
         self = object().__new__(cls)
 
     def __new__(cls, numerator=0, denominator=None):
         self = object().__new__(cls)


@@ -444,9 +514,15 @@ class Rational(Expression, Fraction):
 
     @property
     def constant(self):
 
     @property
     def constant(self):

+        """
+        Return rational as a constant.
+        """

         return self
 
     def isconstant(self):
         return self
 
     def isconstant(self):

+        """
+        Test whether a value is a constant.
+        """

         return True
 
     def __bool__(self):
         return True
 
     def __bool__(self):


@@ -470,6 +546,9 @@ class Rational(Expression, Fraction):
 
     @classmethod
     def fromsympy(cls, expr):
 
     @classmethod
     def fromsympy(cls, expr):

+        """
+        Create a rational object from a sympy expression
+        """

         import sympy
         if isinstance(expr, sympy.Rational):
             return Rational(expr.p, expr.q)
         import sympy
         if isinstance(expr, sympy.Rational):
             return Rational(expr.p, expr.q)

diff --git a/linpy/polyhedra.py b/linpy/polyhedra.py
index e9226f2..8eddb2d 100644 (file)
--- a/linpy/polyhedra.py
+++ b/linpy/polyhedra.py
@@ -35,7 +35,9 @@ __all__ = [
 
 
 class Polyhedron(Domain):
 
 
 class Polyhedron(Domain):

-
+    """
+    Polyhedron class allows users to build and inspect polyherons. Polyhedron inherits from Domain.
+    """

     __slots__ = (
         '_equalities',
         '_inequalities',
     __slots__ = (
         '_equalities',
         '_inequalities',


@@ -45,6 +47,10 @@ class Polyhedron(Domain):
     )
 
     def __new__(cls, equalities=None, inequalities=None):
     )
 
     def __new__(cls, equalities=None, inequalities=None):

+        """
+        Create and return a new Polyhedron from a string or list of equalities and inequalities.
+        """
+        

         if isinstance(equalities, str):
             if inequalities is not None:
                 raise TypeError('too many arguments')
         if isinstance(equalities, str):
             if inequalities is not None:
                 raise TypeError('too many arguments')


@@ -74,21 +80,21 @@ class Polyhedron(Domain):
     @property
     def equalities(self):
         """
     @property
     def equalities(self):
         """

-        Return a list of the equalities in a set.
+        Return a list of the equalities in a polyhedron.

         """
         return self._equalities
 
     @property
     def inequalities(self):
         """
         """
         return self._equalities
 
     @property
     def inequalities(self):
         """

-        Return a list of the inequalities in a set.
+        Return a list of the inequalities in a polyhedron.

         """
         return self._inequalities
 
     @property
     def constraints(self):
         """
         """
         return self._inequalities
 
     @property
     def constraints(self):
         """

-        Return ta list of the constraints of a set.
+        Return the list of the constraints of a polyhedron.

         """
         return self._constraints
 
         """
         return self._constraints
 


@@ -96,15 +102,15 @@ class Polyhedron(Domain):
     def polyhedra(self):
         return self,
 
     def polyhedra(self):
         return self,
 

-    def disjoint(self):
+    def make_disjoint(self):

         """
         """

-        Return a set as disjoint.
+        Return a polyhedron as disjoint.

         """
         return self
 
     def isuniverse(self):
         """
         """
         return self
 
     def isuniverse(self):
         """

-        Return true if a set is the Universe set.
+        Return true if a polyhedron is the Universe set.

         """
         islbset = self._toislbasicset(self.equalities, self.inequalities,
             self.symbols)
         """
         islbset = self._toislbasicset(self.equalities, self.inequalities,
             self.symbols)


@@ -114,11 +120,14 @@ class Polyhedron(Domain):
 
     def aspolyhedron(self):
         """
 
     def aspolyhedron(self):
         """

-        Return polyhedral hull of a set.
+        Return the polyhedral hull of a polyhedron.

         """
         return self
 
     def __contains__(self, point):
         """
         return self
 
     def __contains__(self, point):

+        """
+        Report whether a polyhedron constains an integer point
+        """

         if not isinstance(point, Point):
             raise TypeError('point must be a Point instance')
         if self.symbols != point.symbols:
         if not isinstance(point, Point):
             raise TypeError('point must be a Point instance')
         if self.symbols != point.symbols:


@@ -233,6 +242,9 @@ class Polyhedron(Domain):
 
     @classmethod
     def fromstring(cls, string):
 
     @classmethod
     def fromstring(cls, string):

+        """
+        Create and return a Polyhedron from a string.
+        """

         domain = Domain.fromstring(string)
         if not isinstance(domain, Polyhedron):
             raise ValueError('non-polyhedral expression: {!r}'.format(string))
         domain = Domain.fromstring(string)
         if not isinstance(domain, Polyhedron):
             raise ValueError('non-polyhedral expression: {!r}'.format(string))


@@ -261,7 +273,7 @@ class Polyhedron(Domain):
     @classmethod
     def fromsympy(cls, expr):
         """
     @classmethod
     def fromsympy(cls, expr):
         """

-        Convert a sympy object to an expression.
+        Convert a sympy object to a polyhedron.

         """
         domain = Domain.fromsympy(expr)
         if not isinstance(domain, Polyhedron):
         """
         domain = Domain.fromsympy(expr)
         if not isinstance(domain, Polyhedron):


@@ -270,7 +282,7 @@ class Polyhedron(Domain):
 
     def tosympy(self):
         """
 
     def tosympy(self):
         """

-        Return an expression as a sympy object.
+        Return a polyhedron as a sympy object.

         """
         import sympy
         constraints = []
         """
         import sympy
         constraints = []


@@ -351,41 +363,41 @@ def _polymorphic(func):
 @_polymorphic
 def Lt(left, right):
     """
 @_polymorphic
 def Lt(left, right):
     """

-    Assert first set is less than the second set.
+    Returns a Polyhedron instance with a single constraint as left less than right.

     """
     return Polyhedron([], [right - left - 1])
 
 @_polymorphic
 def Le(left, right):
     """
     """
     return Polyhedron([], [right - left - 1])
 
 @_polymorphic
 def Le(left, right):
     """

-    Assert first set is less than or equal to the second set.
+    Returns a Polyhedron instance with a single constraint as left less than or equal to right.

     """
     return Polyhedron([], [right - left])
 
 @_polymorphic
 def Eq(left, right):
     """
     """
     return Polyhedron([], [right - left])
 
 @_polymorphic
 def Eq(left, right):
     """

-    Assert first set is equal to the second set.
+    Returns a Polyhedron instance with a single constraint as left equal to right.

     """
     return Polyhedron([left - right], [])
 
 @_polymorphic
 def Ne(left, right):
     """
     """
     return Polyhedron([left - right], [])
 
 @_polymorphic
 def Ne(left, right):
     """

-    Assert first set is not equal to the second set.
+    Returns a Polyhedron instance with a single constraint as left not equal to right.

     """
     return ~Eq(left, right)
 
 @_polymorphic
 def Gt(left, right):
     """
     """
     return ~Eq(left, right)
 
 @_polymorphic
 def Gt(left, right):
     """

-    Assert first set is greater than the second set.
+    Returns a Polyhedron instance with a single constraint as left greater than right.

     """
     return Polyhedron([], [left - right - 1])
 
 @_polymorphic
 def Ge(left, right):
     """
     """
     return Polyhedron([], [left - right - 1])
 
 @_polymorphic
 def Ge(left, right):
     """

-    Assert first set is greater than or equal to the second set.
+    Returns a Polyhedron instance with a single constraint as left greater than or equal to right.

     """
     return Polyhedron([], [left - right])
     """
     return Polyhedron([], [left - right])