<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:
 def evaluate(nodes, x_val, y_val):
 r"""Evaluate the implicitized bivariate polynomial containing the curve. Assumes `algebraic curve`_ containing :math:`B(s, t)` is given by :math:`f(x, y) = 0`. This function evaluates :math:`f(x, y)`. .. note:: This assumes, but doesn't check, that ``nodes`` has 2 rows. .. note:: This assumes, but doesn't check, that ``nodes`` is not degree-elevated. If it were degree-elevated, then the Sylvester matrix will always have zero determinant. Args: nodes (numpy.ndarray):
 ``2 x N`` array of nodes in a curve. x_val (float):
 ``x``-coordinate for evaluation. y_val (float):
 ``y``-coordinate for evaluation. Returns: float: The computed value of :math:`f(x, y)`. Raises: ValueError: If the curve is a point. .UnsupportedDegree: If the degree is not 1, 2 or 3. """

    _, num_nodes = nodes.shape
    if num_nodes == 1:
        raise ValueError("A point cannot be implicitized")

    elif num_nodes == 2:
        # x(s) - x = (x0 - x) (1 - s) + (x1 - x) s
        # y(s) - y = (y0 - y) (1 - s) + (y1 - y) s
        # Modified Sylvester: [x0 - x, x1 - x]
        #                     [y0 - y, y1 - y]
        return (nodes[0, 0] - x_val) * (nodes[1, 1] - y_val) - (
            nodes[0, 1] - x_val
        ) * (nodes[1, 0] - y_val)

    elif num_nodes == 3:
        # x(s) - x = (x0 - x) (1 - s)^2 + 2 (x1 - x) s(1 - s) + (x2 - x) s^2
        # y(s) - y = (y0 - y) (1 - s)^2 + 2 (y1 - y) s(1 - s) + (y2 - y) s^2
        # Modified Sylvester: [x0 - x, 2(x1 - x),    x2 - x,      0] = A|B|C|0
        #                     [     0,    x0 - x, 2(x1 - x), x2 - x]   0|A|B|C
        #                     [y0 - y, 2(y1 - y),    y2 - y,      0]   D|E|F|0
        #                     [     0,    y0 - y, 2(y1 - y), y2 - y]   0|D|E|F
        val_a, val_b, val_c = nodes[0, :] - x_val
        val_b *= 2
        val_d, val_e, val_f = nodes[1, :] - y_val
        val_e *= 2
        #     [A, B, C]         [E, F, 0]
        # det [E, F, 0] = - det [A, B, C] = -E (BF - CE) + F(AF - CD)
        #     [D, E, F]         [D, E, F]
        sub1 = val_b * val_f - val_c * val_e
        sub2 = val_a * val_f - val_c * val_d
        sub_det_a = -val_e * sub1 + val_f * sub2
        #     [B, C, 0]
        # det [A, B, C] = B (BF - CE) - C (AF - CD)
        #     [D, E, F]
        sub_det_d = val_b * sub1 - val_c * sub2
        return val_a * sub_det_a + val_d * sub_det_d

    elif num_nodes == 4:
        return _evaluate3(nodes, x_val, y_val)

    else:
        raise _helpers.UnsupportedDegree(num_nodes - 1, supported=(1, 2, 3))