Polyhedra Module
================

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

.. py:class:: Polyhedron(Domain)

    .. 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.

    .. attribute:: inequalities

        Returns a list of the inequalities in a polyhedron.

    .. attribute:: constraints

        Returns a list of the constraints of a polyhedron.

    .. py:method:: make_disjoint(self)

        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)

        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.

.. py:function:: Eq(left, right)

   Returns a Polyhedron instance with a single constraint as *left* equal to *right*.

.. py:function:: Ne(left, right)

   Returns a Polyhedron instance with a single constraint as *left* not equal to *right*.

.. py:function:: Lt(left, right)

   Returns a Polyhedron instance with a single constraint as *left* less than *right*.

.. py:function:: Le(left, right)

   Returns a Polyhedron instance with a single constraint as *left* less than or equal to *right*.

.. py:function:: Gt(left, right)

   Returns a Polyhedron instance with a single constraint as *left* greater than *right*.

.. py:function:: Ge(left, right)

   Returns a Polyhedron instance with a single constraint as *left* greater than or equal to *right*.