index e5e2523..bfc7efe 100644 (file)
@@ -144,6 +144,15 @@ class Polyhedron(Domain):
def aspolyhedron(self):
return self

+    def convex_union(self, *others):
+        """
+        Return the convex union of two or more polyhedra.
+        """
+        for other in others:
+            if not isinstance(other, Polyhedron):
+                raise TypeError('arguments must be Polyhedron instances')
+        return Polyhedron(self.union(*others))
+
def __contains__(self, point):
if not isinstance(point, Point):
raise TypeError('point must be a Point instance')
@@ -164,7 +173,11 @@ class Polyhedron(Domain):
for inequality in self.inequalities]
return Polyhedron(equalities, inequalities)

-    def _asinequalities(self):
+    def asinequalities(self):
+        """
+        Express the polyhedron using inequalities, given as a list of
+        expressions greater or equal to 0.
+        """
inequalities = list(self.equalities)
inequalities.extend([-expression for expression in self.equalities])
inequalities.extend(self.inequalities)
@@ -179,8 +192,8 @@ class Polyhedron(Domain):
"""
if not isinstance(other, Polyhedron):
raise TypeError('argument must be a Polyhedron instance')
-        inequalities1 = self._asinequalities()
-        inequalities2 = other._asinequalities()
+        inequalities1 = self.asinequalities()
+        inequalities2 = other.asinequalities()
inequalities = []
for inequality1 in inequalities1:
if other <= Polyhedron(inequalities=[inequality1]):
@@ -268,9 +281,33 @@ 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:
@@ -351,63 +388,77 @@ class UniverseType(Polyhedron):
Universe = UniverseType()

-def _polymorphic(func):
+def _pseudoconstructor(func):
@functools.wraps(func)
-    def wrapper(left, right):
-        if not isinstance(left, LinExpr):
-            if isinstance(left, numbers.Rational):
-                left = Rational(left)
-            else:
-                raise TypeError('left must be a a rational number '
-                    'or a linear expression')
-        if not isinstance(right, LinExpr):
-            if isinstance(right, numbers.Rational):
-                right = Rational(right)
-            else:
-                raise TypeError('right must be a a rational number '
-                    'or a linear expression')
-        return func(left, right)
+    def wrapper(expr1, expr2, *exprs):
+        exprs = (expr1, expr2) + exprs
+        for expr in exprs:
+            if not isinstance(expr, LinExpr):
+                if isinstance(expr, numbers.Rational):
+                    expr = Rational(expr)
+                else:
+                    raise TypeError('arguments must be rational numbers '
+                        'or linear expressions')
+        return func(*exprs)
return wrapper

-@_polymorphic
-def Lt(left, right):
+@_pseudoconstructor
+def Lt(*exprs):
"""
Create the polyhedron with constraints expr1 < expr2 < expr3 ...
"""
-    return Polyhedron([], [right - left - 1])
+    inequalities = []
+    for left, right in zip(exprs, exprs[1:]):
+        inequalities.append(right - left - 1)
+    return Polyhedron([], inequalities)

-@_polymorphic
-def Le(left, right):
+@_pseudoconstructor
+def Le(*exprs):
"""
Create the polyhedron with constraints expr1 <= expr2 <= expr3 ...
"""
-    return Polyhedron([], [right - left])
+    inequalities = []
+    for left, right in zip(exprs, exprs[1:]):
+        inequalities.append(right - left)
+    return Polyhedron([], inequalities)

-@_polymorphic
-def Eq(left, right):
+@_pseudoconstructor
+def Eq(*exprs):
"""
Create the polyhedron with constraints expr1 == expr2 == expr3 ...
"""
-    return Polyhedron([left - right], [])
+    equalities = []
+    for left, right in zip(exprs, exprs[1:]):
+        equalities.append(left - right)
+    return Polyhedron(equalities, [])

-@_polymorphic
-def Ne(left, right):
+@_pseudoconstructor
+def Ne(*exprs):
"""
Create the domain such that expr1 != expr2 != expr3 ... The result is a
-    Domain, not a Polyhedron.
+    Domain object, not a Polyhedron.
"""
-    return ~Eq(left, right)
+    domain = Universe
+    for left, right in zip(exprs, exprs[1:]):
+        domain &= ~Eq(left, right)
+    return domain

-@_polymorphic
-def Ge(left, right):
+@_pseudoconstructor
+def Ge(*exprs):
"""
Create the polyhedron with constraints expr1 >= expr2 >= expr3 ...
"""
-    return Polyhedron([], [left - right])
+    inequalities = []
+    for left, right in zip(exprs, exprs[1:]):
+        inequalities.append(left - right)
+    return Polyhedron([], inequalities)

-@_polymorphic
-def Gt(left, right):
+@_pseudoconstructor
+def Gt(*exprs):
"""
Create the polyhedron with constraints expr1 > expr2 > expr3 ...
"""
-    return Polyhedron([], [left - right - 1])
+    inequalities = []
+    for left, right in zip(exprs, exprs[1:]):
+        inequalities.append(left - right - 1)
+    return Polyhedron([], inequalities)