LinExpr() accepts rational numbers

[linpy.git] / linpy / polyhedra.py

diff --git a/linpy/polyhedra.py b/linpy/polyhedra.py
index a720b74..ead9b83 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
 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__ = (
     """
 
     __slots__ = (


@@ -56,28 +57,31 @@ class Polyhedron(Domain):
         0 <= x <= 2, 0 <= y <= 2 can be constructed with:
 
         >>> x, y = symbols('x y')
         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')
 
         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.
 
 
         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:
 
 
         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:
         """
         if isinstance(equalities, str):
             if inequalities is not None:


@@ -90,15 +94,23 @@ class Polyhedron(Domain):
         sc_equalities = []
         if equalities is not None:
             for equality in equalities:
         sc_equalities = []
         if equalities is not None:
             for equality in equalities:

-                if not isinstance(equality, LinExpr):
-                    raise TypeError('equalities must be linear expressions')
-                sc_equalities.append(equality.scaleint())
+                if isinstance(equality, LinExpr):
+                    sc_equalities.append(equality.scaleint())
+                elif isinstance(equality, numbers.Rational):
+                    sc_equalities.append(Rational(equality).scaleint())
+                else:
+                    raise TypeError('equalities must be linear expressions '
+                        'or rational numbers')

         sc_inequalities = []
         if inequalities is not None:
             for inequality in inequalities:
         sc_inequalities = []
         if inequalities is not None:
             for inequality in inequalities:

-                if not isinstance(inequality, LinExpr):
-                    raise TypeError('inequalities must be linear expressions')
-                sc_inequalities.append(inequality.scaleint())
+                if isinstance(inequality, LinExpr):
+                    sc_inequalities.append(inequality.scaleint())
+                elif isinstance(inequality, numbers.Rational):
+                    sc_inequalities.append(Rational(inequality).scaleint())
+                else:
+                    raise TypeError('inequalities must be linear expressions '
+                        'or rational numbers')

         symbols = cls._xsymbols(sc_equalities + sc_inequalities)
         islbset = cls._toislbasicset(sc_equalities, sc_inequalities, symbols)
         return cls._fromislbasicset(islbset, symbols)
         symbols = cls._xsymbols(sc_equalities + sc_inequalities)
         islbset = cls._toislbasicset(sc_equalities, sc_inequalities, symbols)
         return cls._fromislbasicset(islbset, symbols)


@@ -281,27 +293,43 @@ class Polyhedron(Domain):
     def __repr__(self):
         strings = []
         for equality in self.equalities:
     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:
         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:
             return 'And({})'.format(', '.join(strings))
 
         if len(strings) == 1:
             return strings[0]
         else:
             return 'And({})'.format(', '.join(strings))
 

-    def _repr_latex_(self):
-        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
     @classmethod

-    def fromsympy(cls, expr):
-        domain = Domain.fromsympy(expr)
+    def fromsympy(cls, expression):
+        domain = Domain.fromsympy(expression)

         if not isinstance(domain, Polyhedron):
         if not isinstance(domain, Polyhedron):

-            raise ValueError('non-polyhedral expression: {!r}'.format(expr))
+            raise ValueError('non-polyhedral expression: {!r}'.format(expression))

         return domain
 
     def tosympy(self):
         return domain
 
     def tosympy(self):


@@ -335,9 +363,6 @@ class EmptyType(Polyhedron):
     def __repr__(self):
         return 'Empty'
 
     def __repr__(self):
         return 'Empty'
 

-    def _repr_latex_(self):
-        return '$$\\emptyset$$'
-

 Empty = EmptyType()
 
 
 Empty = EmptyType()
 
 


@@ -358,83 +383,80 @@ class UniverseType(Polyhedron):
     def __repr__(self):
         return 'Universe'
 
     def __repr__(self):
         return 'Universe'
 

-    def _repr_latex_(self):
-        return '$$\\Omega$$'
-

 Universe = UniverseType()
 
 
 def _pseudoconstructor(func):
     @functools.wraps(func)
 Universe = UniverseType()
 
 
 def _pseudoconstructor(func):
     @functools.wraps(func)

-    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)
+    def wrapper(expression1, expression2, *expressions):
+        expressions = (expression1, expression2) + expressions
+        for expression in expressions:
+            if not isinstance(expression, LinExpr):
+                if isinstance(expression, numbers.Rational):
+                    expression = Rational(expression)

                 else:
                     raise TypeError('arguments must be rational numbers '
                         'or linear expressions')
                 else:
                     raise TypeError('arguments must be rational numbers '
                         'or linear expressions')

-        return func(*exprs)
+        return func(*expressions)

     return wrapper
 
 @_pseudoconstructor
     return wrapper
 
 @_pseudoconstructor

-def Lt(*exprs):
+def Lt(*expressions):

     """
     Create the polyhedron with constraints expr1 < expr2 < expr3 ...
     """
     inequalities = []
     """
     Create the polyhedron with constraints expr1 < expr2 < expr3 ...
     """
     inequalities = []

-    for left, right in zip(exprs, exprs[1:]):
+    for left, right in zip(expressions, expressions[1:]):

         inequalities.append(right - left - 1)
     return Polyhedron([], inequalities)
 
 @_pseudoconstructor
         inequalities.append(right - left - 1)
     return Polyhedron([], inequalities)
 
 @_pseudoconstructor

-def Le(*exprs):
+def Le(*expressions):

     """
     Create the polyhedron with constraints expr1 <= expr2 <= expr3 ...
     """
     inequalities = []
     """
     Create the polyhedron with constraints expr1 <= expr2 <= expr3 ...
     """
     inequalities = []

-    for left, right in zip(exprs, exprs[1:]):
+    for left, right in zip(expressions, expressions[1:]):

         inequalities.append(right - left)
     return Polyhedron([], inequalities)
 
 @_pseudoconstructor
         inequalities.append(right - left)
     return Polyhedron([], inequalities)
 
 @_pseudoconstructor

-def Eq(*exprs):
+def Eq(*expressions):

     """
     Create the polyhedron with constraints expr1 == expr2 == expr3 ...
     """
     equalities = []
     """
     Create the polyhedron with constraints expr1 == expr2 == expr3 ...
     """
     equalities = []

-    for left, right in zip(exprs, exprs[1:]):
+    for left, right in zip(expressions, expressions[1:]):

         equalities.append(left - right)
     return Polyhedron(equalities, [])
 
 @_pseudoconstructor
         equalities.append(left - right)
     return Polyhedron(equalities, [])
 
 @_pseudoconstructor

-def Ne(*exprs):
+def Ne(*expressions):

     """
     Create the domain such that expr1 != expr2 != expr3 ... The result is a
     Domain object, not a Polyhedron.
     """
     domain = Universe
     """
     Create the domain such that expr1 != expr2 != expr3 ... The result is a
     Domain object, not a Polyhedron.
     """
     domain = Universe

-    for left, right in zip(exprs, exprs[1:]):
+    for left, right in zip(expressions, expressions[1:]):

         domain &= ~Eq(left, right)
     return domain
 
 @_pseudoconstructor
         domain &= ~Eq(left, right)
     return domain
 
 @_pseudoconstructor

-def Ge(*exprs):
+def Ge(*expressions):

     """
     Create the polyhedron with constraints expr1 >= expr2 >= expr3 ...
     """
     inequalities = []
     """
     Create the polyhedron with constraints expr1 >= expr2 >= expr3 ...
     """
     inequalities = []

-    for left, right in zip(exprs, exprs[1:]):
+    for left, right in zip(expressions, expressions[1:]):

         inequalities.append(left - right)
     return Polyhedron([], inequalities)
 
 @_pseudoconstructor
         inequalities.append(left - right)
     return Polyhedron([], inequalities)
 
 @_pseudoconstructor

-def Gt(*exprs):
+def Gt(*expressions):

     """
     Create the polyhedron with constraints expr1 > expr2 > expr3 ...
     """
     inequalities = []
     """
     Create the polyhedron with constraints expr1 > expr2 > expr3 ...
     """
     inequalities = []

-    for left, right in zip(exprs, exprs[1:]):
+    for left, right in zip(expressions, expressions[1:]):

         inequalities.append(left - right - 1)
     return Polyhedron([], inequalities)
         inequalities.append(left - right - 1)
     return Polyhedron([], inequalities)