Add sage code

lib/tait_coloring.py

@@ -0,0 +1,18 @@
+"""Utilities for computing Tait colorings from vertex colorings of the dual graph."""
+from typing import Any, cast
+from sage.all import Graph
+from lib.edge_for_dual_edge import get_edge_for_dual_edge
+
+def get_tait_coloring(planar_dual: Graph, coloring: dict[Any, int]) -> dict[Any, int]:
+    """Return a Tait (edge 3-coloring) from a vertex 4-coloring of the dual graph."""
+    tait_coloring: dict[Any, int] = {}
+    for dual_edge in cast(list[Any], planar_dual.edges()):  # type: ignore
+        edge = get_edge_for_dual_edge(dual_edge)
+        colors = {coloring[edge[0]], coloring[edge[1]]}
+        if colors in ({0, 1}, {2, 3}):
+            tait_coloring[dual_edge] = 0
+        elif colors in ({1, 2}, {0, 3}):
+            tait_coloring[dual_edge] = 1
+        else:
+            tait_coloring[dual_edge] = 2
+    return tait_coloring