Linear Expression Module
========================

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:: coefficients(self)
        
        Return a list of the coefficients of an expression
        
    .. attribute:: constant
    
        Return the constant value of an expression.
        
    .. attribute:: symbols
    
        Return a list of symbols in an expression.                            
    
    .. attribute:: dimension
    
        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:: __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:: fromstring(self)
    
        Create an expression from a string.

    .. py:method:: fromsympy(self)
    
        Convert sympy object to an expression.
        
    .. py:method:: tosympy(self)
    
        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)

    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