Mention that we use Z-polyhedra

[linpy.git] / linpy / polyhedra.py

diff --git a/linpy/polyhedra.py b/linpy/polyhedra.py
index a720b74..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:
@@ -281,9 +285,33 @@ class Polyhedron(Domain):
     def __repr__(self):
         strings = []
         for equality in self.equalities:
-            strings.append('Eq({}, 0)'.format(equality))
+            left, right, swap = 0, 0, False
+            for i, (symbol, coefficient) in enumerate(equality.coefficients()):
+                if coefficient > 0:
+                    left += coefficient * symbol
+                else:
+                    right -= coefficient * symbol
+                    if i == 0:
+                        swap = True
+            if equality.constant > 0:
+                left += equality.constant
+            else:
+                right -= equality.constant
+            if swap:
+                left, right = right, left
+            strings.append('{} == {}'.format(left, right))
         for inequality in self.inequalities:
-            strings.append('Ge({}, 0)'.format(inequality))
+            left, right = 0, 0
+            for symbol, coefficient in inequality.coefficients():
+                if coefficient < 0:
+                    left -= coefficient * symbol
+                else:
+                    right += coefficient * symbol
+            if inequality.constant < 0:
+                left -= inequality.constant
+            else:
+                right += inequality.constant
+            strings.append('{} <= {}'.format(left, right))
         if len(strings) == 1:
             return strings[0]
         else: