Simplify Expression.__mul__(), Expression.__truediv__()

[linpy.git] / pypol / polyhedra.py

diff --git a/pypol/polyhedra.py b/pypol/polyhedra.py
index 3db8f40..6b5f9ab 100644 (file)
--- a/pypol/polyhedra.py
+++ b/pypol/polyhedra.py
@@ -1,4 +1,3 @@
-

 import functools
 import math
 import numbers
 import functools
 import math
 import numbers


@@ -6,6 +5,7 @@ import numbers
 from . import islhelper
 
 from .islhelper import mainctx, libisl
 from . import islhelper
 
 from .islhelper import mainctx, libisl

+from .geometry import GeometricObject, Point, Vector

 from .linexprs import Expression, Symbol, Rational
 from .domains import Domain
 
 from .linexprs import Expression, Symbol, Rational
 from .domains import Domain
 


@@ -32,11 +32,7 @@ class Polyhedron(Domain):
             if inequalities is not None:
                 raise TypeError('too many arguments')
             return cls.fromstring(equalities)
             if inequalities is not None:
                 raise TypeError('too many arguments')
             return cls.fromstring(equalities)

-        elif isinstance(equalities, Polyhedron):
-            if inequalities is not None:
-                raise TypeError('too many arguments')
-            return equalities
-        elif isinstance(equalities, Domain):
+        elif isinstance(equalities, GeometricObject):

             if inequalities is not None:
                 raise TypeError('too many arguments')
             return equalities.aspolyhedron()
             if inequalities is not None:
                 raise TypeError('too many arguments')
             return equalities.aspolyhedron()


@@ -87,6 +83,19 @@ class Polyhedron(Domain):
     def aspolyhedron(self):
         return self
 
     def aspolyhedron(self):
         return self
 

+    def __contains__(self, point):
+        if not isinstance(point, Point):
+            raise TypeError('point must be a Point instance')
+        if self.symbols != point.symbols:
+            raise ValueError('arguments must belong to the same space')
+        for equality in self.equalities:
+            if equality.subs(point.coordinates()) != 0:
+                return False
+        for inequality in self.inequalities:
+            if inequality.subs(point.coordinates()) < 0:
+                return False
+        return True
+

     def subs(self, symbol, expression=None):
         equalities = [equality.subs(symbol, expression)
             for equality in self.equalities]
     def subs(self, symbol, expression=None):
         equalities = [equality.subs(symbol, expression)
             for equality in self.equalities]


@@ -173,14 +182,27 @@ class Polyhedron(Domain):
         else:
             strings = []
             for equality in self.equalities:
         else:
             strings = []
             for equality in self.equalities:

-                strings.append('0 == {}'.format(equality))
+                strings.append('Eq({}, 0)'.format(equality))

             for inequality in self.inequalities:
             for inequality in self.inequalities:

-                strings.append('0 <= {}'.format(inequality))
+                strings.append('Ge({}, 0)'.format(inequality))

             if len(strings) == 1:
                 return strings[0]
             else:
                 return 'And({})'.format(', '.join(strings))
 
             if len(strings) == 1:
                 return strings[0]
             else:
                 return 'And({})'.format(', '.join(strings))
 

+    def _repr_latex_(self):
+        if self.isempty():
+            return '$\\emptyset$'
+        elif self.isuniverse():
+            return '$\\Omega$'
+        else:
+            strings = []
+            for equality in self.equalities:
+                strings.append('{} = 0'.format(equality._repr_latex_().strip('$')))
+            for inequality in self.inequalities:
+                strings.append('{} \\ge 0'.format(inequality._repr_latex_().strip('$')))
+            return '${}$'.format(' \\wedge '.join(strings))
+

     @classmethod
     def fromsympy(cls, expr):
         domain = Domain.fromsympy(expr)
     @classmethod
     def fromsympy(cls, expr):
         domain = Domain.fromsympy(expr)


@@ -197,16 +219,26 @@ class Polyhedron(Domain):
             constraints.append(sympy.Ge(inequality.tosympy(), 0))
         return sympy.And(*constraints)
 
             constraints.append(sympy.Ge(inequality.tosympy(), 0))
         return sympy.And(*constraints)
 

+    @classmethod
+    def _polygon_inner_point(cls, points):
+        symbols = points[0].symbols
+        coordinates = {symbol: 0 for symbol in symbols}
+        for point in points:
+            for symbol, coordinate in point.coordinates():
+                coordinates[symbol] += coordinate
+        for symbol in symbols:
+            coordinates[symbol] /= len(points)
+        return Point(coordinates)
+

     @classmethod
     def _sort_polygon_2d(cls, points):
         if len(points) <= 3:
             return points
     @classmethod
     def _sort_polygon_2d(cls, points):
         if len(points) <= 3:
             return points

-        o = sum((Vector(point) for point in points)) / len(points)
-        o = Point(o.coordinates())
+        o = cls._polygon_inner_point(points)

         angles = {}
         for m in points:
             om = Vector(o, m)
         angles = {}
         for m in points:
             om = Vector(o, m)

-            dx, dy = (coordinate for symbol, coordinates in om.coordinates())
+            dx, dy = (coordinate for symbol, coordinate in om.coordinates())

             angle = math.atan2(dy, dx)
             angles[m] = angle
         return sorted(points, key=angles.get)
             angle = math.atan2(dy, dx)
             angles[m] = angle
         return sorted(points, key=angles.get)


@@ -215,13 +247,18 @@ class Polyhedron(Domain):
     def _sort_polygon_3d(cls, points):
         if len(points) <= 3:
             return points
     def _sort_polygon_3d(cls, points):
         if len(points) <= 3:
             return points

-        o = sum((Vector(point) for point in points)) / len(points)
-        o = Point(o.coordinates())
-        a, b = points[:2]
+        o = cls._polygon_inner_point(points)
+        a = points[0]

         oa = Vector(o, a)
         oa = Vector(o, a)

-        ob = Vector(o, b)

         norm_oa = oa.norm()
         norm_oa = oa.norm()

-        u = (oa.cross(ob)).asunit()
+        for b in points[1:]:
+            ob = Vector(o, b)
+            u = oa.cross(ob)
+            if not u.isnull():
+                u = u.asunit()
+                break
+        else:
+            raise ValueError('degenerate polygon')

         angles = {a: 0.}
         for m in points[1:]:
             om = Vector(o, m)
         angles = {a: 0.}
         for m in points[1:]:
             om = Vector(o, m)


@@ -233,6 +270,17 @@ class Polyhedron(Domain):
             angles[m] = angle
         return sorted(points, key=angles.get)
 
             angles[m] = angle
         return sorted(points, key=angles.get)
 

+    def faces(self):
+        vertices = self.vertices()
+        faces = []
+        for constraint in self.constraints:
+            face = []
+            for vertex in vertices:
+                if constraint.subs(vertex.coordinates()) == 0:
+                    face.append(vertex)
+            faces.append(face)
+        return faces
+

     def plot(self):
         import matplotlib.pyplot as plt
         from matplotlib.path import Path
     def plot(self):
         import matplotlib.pyplot as plt
         from matplotlib.path import Path


@@ -276,16 +324,18 @@ class Polyhedron(Domain):
 def _polymorphic(func):
     @functools.wraps(func)
     def wrapper(left, right):
 def _polymorphic(func):
     @functools.wraps(func)
     def wrapper(left, right):

-        if isinstance(left, numbers.Rational):
-            left = Rational(left)
-        elif not isinstance(left, Expression):
-            raise TypeError('left must be a a rational number '
-                'or a linear expression')
-        if isinstance(right, numbers.Rational):
-            right = Rational(right)
-        elif not isinstance(right, Expression):
-            raise TypeError('right must be a a rational number '
-                'or a linear expression')
+        if not isinstance(left, Expression):
+            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, Expression):
+            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)
     return wrapper
 
         return func(left, right)
     return wrapper