Mention that we use Z-polyhedra

[linpy.git] / linpy / polyhedra.py

diff --git a/linpy/polyhedra.py b/linpy/polyhedra.py
index bfc7efe..f802151 100644 (file)
--- a/linpy/polyhedra.py
+++ b/linpy/polyhedra.py
@@ -37,8 +37,9 @@ __all__ = [
 class Polyhedron(Domain):
     """
     A convex polyhedron (or simply "polyhedron") is the space defined by a
-    system of linear equalities and inequalities. This space can be
-    unbounded.
+    system of linear equalities and inequalities. This space can be unbounded. A
+    Z-polyhedron (simply called "polyhedron" in LinPy) is the set of integer
+    points in a convex polyhedron.
     """
 
     __slots__ = (
@@ -56,28 +57,31 @@ class Polyhedron(Domain):
         0 <= x <= 2, 0 <= y <= 2 can be constructed with:
 
         >>> x, y = symbols('x y')
-        >>> square = Polyhedron([], [x, 2 - x, y, 2 - y])
+        >>> square1 = Polyhedron([], [x, 2 - x, y, 2 - y])
+        >>> square1
+        And(0 <= x, x <= 2, 0 <= y, y <= 2)
 
         It may be easier to use comparison operators LinExpr.__lt__(),
         LinExpr.__le__(), LinExpr.__ge__(), LinExpr.__gt__(), or functions Lt(),
         Le(), Eq(), Ge() and Gt(), using one of the following instructions:
 
         >>> x, y = symbols('x y')
-        >>> square = (0 <= x) & (x <= 2) & (0 <= y) & (y <= 2)
-        >>> square = Le(0, x, 2) & Le(0, y, 2)
+        >>> square1 = (0 <= x) & (x <= 2) & (0 <= y) & (y <= 2)
+        >>> square1 = Le(0, x, 2) & Le(0, y, 2)
 
         It is also possible to build a polyhedron from a string.
 
-        >>> square = Polyhedron('0 <= x <= 2, 0 <= y <= 2')
+        >>> square1 = Polyhedron('0 <= x <= 2, 0 <= y <= 2')
 
         Finally, a polyhedron can be constructed from a GeometricObject
         instance, calling the GeometricObject.aspolyedron() method. This way, it
         is possible to compute the polyhedral hull of a Domain instance, i.e.,
         the convex hull of two polyhedra:
 
-        >>> square = Polyhedron('0 <= x <= 2, 0 <= y <= 2')
-        >>> square2 = Polyhedron('2 <= x <= 4, 2 <= y <= 4')
-        >>> Polyhedron(square | square2)
+        >>> square1 = Polyhedron('0 <= x <= 2, 0 <= y <= 2')
+        >>> square2 = Polyhedron('1 <= x <= 3, 1 <= y <= 3')
+        >>> Polyhedron(square1 | square2)
+        And(0 <= x, 0 <= y, x <= y + 2, y <= x + 2, x <= 3, y <= 3)
         """
         if isinstance(equalities, str):
             if inequalities is not None: