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Given a LineString and a Polygon, detect which Polygon nodes are above or below the LineString

I have a Shapely Polygon and a LineString. I want to be able to determine which Polygon points are above the LineString and which are below. Alternatively, it would also be alright if I were to splice a Polygon using a LineString and generate two new Polygons.

Are there any built-in Shapely methods that would allow me to do this?