def test_best_origin():
expr1 = y ** 2 * x ** 5 + y ** 5 * x ** 7 + 7 * x + x ** 12 + y ** 7 * x
l1 = Segment2D(Point(0, 3), Point(1, 1))
l2 = Segment2D(Point(S(3) / 2, 0), Point(S(3) / 2, 3))
l3 = Segment2D(Point(0, S(3) / 2), Point(3, S(3) / 2))
l4 = Segment2D(Point(0, 2), Point(2, 0))
l5 = Segment2D(Point(0, 2), Point(1, 1))
l6 = Segment2D(Point(2, 0), Point(1, 1))
assert best_origin((2, 1), 3, l1, expr1) == (0, 3)
assert best_origin((2, 0), 3, l2, x ** 7) == (S(3) / 2, 0)
assert best_origin((0, 2), 3, l3, x ** 7) == (0, S(3) / 2)
assert best_origin((1, 1), 2, l4, x ** 7 * y ** 3) == (0, 2)
assert best_origin((1, 1), 2, l4, x ** 3 * y ** 7) == (2, 0)
assert best_origin((1, 1), 2, l5, x ** 2 * y ** 9) == (0, 2)
assert best_origin((1, 1), 2, l6, x ** 9 * y ** 2) == (2, 0)
def test_best_origin():
expr1 = y ** 2 * x ** 5 + y ** 5 * x ** 7 + 7 * x + x ** 12 + y ** 7 * x
l1 = Segment2D(Point(0, 3), Point(1, 1))
l2 = Segment2D(Point(S(3) / 2, 0), Point(S(3) / 2, 3))
l3 = Segment2D(Point(0, S(3) / 2), Point(3, S(3) / 2))
l4 = Segment2D(Point(0, 2), Point(2, 0))
l5 = Segment2D(Point(0, 2), Point(1, 1))
l6 = Segment2D(Point(2, 0), Point(1, 1))
assert best_origin((2, 1), 3, l1, expr1) == (0, 3)
assert best_origin((2, 0), 3, l2, x ** 7) == (S(3) / 2, 0)
assert best_origin((0, 2), 3, l3, x ** 7) == (0, S(3) / 2)
assert best_origin((1, 1), 2, l4, x ** 7 * y ** 3) == (0, 2)
assert best_origin((1, 1), 2, l4, x ** 3 * y ** 7) == (2, 0)
assert best_origin((1, 1), 2, l5, x ** 2 * y ** 9) == (0, 2)
assert best_origin((1, 1), 2, l6, x ** 9 * y ** 2) == (2, 0)