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:
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: