Add compat function index_by_point and point_by_index for edge.

tat/compat.py

@@ -267,17 +267,9 @@ def parity(int_parity: int) -> bool:
 # Segment index
 
 
-def _get_index_for_position(position: tuple[typing.Any, int], edge: E) -> int:
-    sym, index = position
-    if not isinstance(sym, tuple):
-        sym = (sym,)
-    return next(total_index for total_index in range(edge.dimension) if all(
-        sub_sym == sub_symmetry[total_index] for sub_sym, sub_symmetry in zip(sym, edge.symmetry))) + index
-
-
 @T._prepare_position.register  # pylint: disable=protected-access,no-member
 def _(self: T, position: dict[str, tuple[typing.Any, int]]) -> tuple[int, ...]:
-    return tuple(_get_index_for_position(position[name], edge) for name, edge in zip(self.names, self.edges))
+    return tuple(index_by_point(edge, position[name]) for name, edge in zip(self.names, self.edges))
 
 
 # Function renames
@@ -323,6 +315,28 @@ def exponential(self: T, pairs: set[tuple[str, str]], step: int | None = None) -
     return origin_exponential(self, pairs)
 
 
+# Edge point conversion
+
+
+@_compat_function(E)
+def index_by_point(self: E, point: tuple[typing.Any, int]) -> int:
+    "Get index by point on an edge"
+    sym, sub_index = point
+    if not isinstance(sym, tuple):
+        sym = (sym,)
+    return next(total_index for total_index in range(self.dimension) if all(
+        sub_sym == sub_symmetry[total_index] for sub_sym, sub_symmetry in zip(sym, self.symmetry))) + sub_index
+
+
+@_compat_function(E)
+def point_by_index(self: E, index: int) -> tuple[typing.Any, int]:
+    "Get point by index on an edge"
+    sym = tuple(sub_symmetry[index] for sub_symmetry in self.symmetry)
+    sub_index = sum(
+        1 for i in range(index) if all(sub_sym == sub_symmetry[i] for sub_sym, sub_symmetry in zip(sym, self.symmetry)))
+    return sym, sub_index
+
+
 # Random utility