code: def _to_power_basis12(nodes1, nodes2):
      r
      # We manually invert the Vandermonde matrix:
      # [1 0   0  ][c0] = [n0]
      # [1 1/2 1/4][c1]   [n1]
      # [1 1   1  ][c2]   [n2]
      val0 = eval_intersection_polynomial(nodes1, nodes2, 0.0)
      val1 = eval_intersection_polynomial(nodes1, nodes2, 0.5)
      val2 = eval_intersection_polynomial(nodes1, nodes2, 1.0)
      # [c0] = [ 1  0  0][n0]
      # [c1] = [-3  4 -1][n1]
      # [c2] = [ 2 -4  2][n2]
      return np.asfortranarray(
          [
              val0,
              -3.0 * val0 + 4.0 * val1 - val2,
              2.0 * val0 - 4.0 * val1 + 2.0 * val2,
          ]
      )
docs: r"""Compute the coefficients of an **intersection polynomial**.
  
      Helper for :func:`to_power_basis` in the case that the first curve is
      degree one and the second is degree two. In this case, B |eacute|
      zout's `theorem`_ tells us that the **intersection polynomial** is
      degree :math:`1 \cdot 2` hence we return three coefficients.
  
      Args:
          nodes1 (numpy.ndarray): The nodes in the first curve.
          nodes2 (numpy.ndarray): The nodes in the second curve.
  
      Returns:
          numpy.ndarray: ``3``-array of coefficients.