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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def intersect(self, other, strategy=_STRATEGY.GEOMETRIC, _verify=True):
 """Find the common intersection with another surface. Args: other (Surface):
 Other surface to intersect with. strategy (Optional[~bezier.curve.IntersectionStrategy]):
 The intersection algorithm to use. Defaults to geometric. _verify (Optional[bool]):
 Indicates if extra caution should be used to verify assumptions about the algorithm as it proceeds. Can be disabled to speed up execution time. Defaults to :data:`True`. Returns: List[Union[~bezier.curved_polygon.CurvedPolygon, \ ~bezier.surface.Surface]]: List of intersections (possibly empty). Raises: TypeError: If ``other`` is not a surface (and ``_verify=True``). NotImplementedError: If at least one of the surfaces isn't two-dimensional (and ``_verify=True``). ValueError: If ``strategy`` is not a valid :class:`.IntersectionStrategy`. """

        if _verify:
            if not isinstance(other, Surface):
                raise TypeError(
                    "Can only intersect with another surface",
                    "Received",
                    other,
                )

            if self._dimension != 2 or other._dimension != 2:
                raise NotImplementedError(
                    "Intersection only implemented in 2D"
                )

        if strategy == _STRATEGY.GEOMETRIC:
            do_intersect = _surface_intersection.geometric_intersect
        elif strategy == _STRATEGY.ALGEBRAIC:
            do_intersect = _surface_intersection.algebraic_intersect
        else:
            raise ValueError("Unexpected strategy.", strategy)

        edge_infos, contained, all_edge_nodes = do_intersect(
            self._nodes, self._degree, other._nodes, other._degree, _verify
        )
        if edge_infos is None:
            if contained:
                return [self]

            else:
                return [other]

        else:
            return [
                _make_intersection(edge_info, all_edge_nodes)
                for edge_info in edge_infos
            ]