Add sage code

lib/dual_graph.py

@@ -0,0 +1,29 @@
+"""Utilities for working with planar dual graphs."""
+from typing import Any
+from sage.all import Graph
+
+
+def find_vertex_for_dual_face(dual_face: Any) -> Any | None:
+    """Return the primal vertex shared by all faces in the dual face, or None."""
+    shared_vertices = None
+    for dual_edge in dual_face:
+        vertices = set(map(lambda e: e[0], dual_edge[0]))
+        if shared_vertices:
+            shared_vertices.intersection_update(vertices)
+        else:
+            shared_vertices = vertices
+        if len(shared_vertices) == 1:
+            return shared_vertices.pop()
+    return None
+
+
+def _dual_edge_has_vertex(dual_edge: Any, vertex: Any) -> bool:
+    return any(vertex in edge for dual_vertex in dual_edge for edge in dual_vertex)
+
+
+def find_dual_face_for_removed_vertex(planar_dual: Graph, vertex: Any) -> Any | None:
+    """Return the dual face of length 5 whose every dual edge contains the given vertex."""
+    for dual_face in list[Any](planar_dual.faces()):  # type: ignore[call-arg]
+        if len(dual_face) == 5 and all(_dual_edge_has_vertex(de, vertex) for de in dual_face):
+            return dual_face
+    return None