Initial version of AR quivers.

sagemath · Jan 31, 2024 · b207c56 · b207c56
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diff --git a/src/doc/en/reference/quivers/index.rst b/src/doc/en/reference/quivers/index.rst
@@ -6,6 +6,7 @@ Quivers
 
    sage/quivers/algebra
    sage/quivers/algebra_elements
+   sage/quivers/ar_quiver
    sage/quivers/homspace
    sage/quivers/morphism
    sage/quivers/path_semigroup

diff --git a/src/sage/graphs/digraph.py b/src/sage/graphs/digraph.py
@@ -70,6 +70,7 @@
     :delim: |
 
     :meth:`~DiGraph.path_semigroup` | Return the (partial) semigroup formed by the paths of the digraph.
+    :meth:`~DiGraph.auslander_reiten_quiver` | Return the Auslander-Reiten quiver of ``self``.
 
 **Connectivity:**
 
@@ -3180,6 +3181,23 @@ def path_semigroup(self):
         from sage.quivers.path_semigroup import PathSemigroup
         return PathSemigroup(self)
 
+    def auslander_reiten_quiver(self):
+        r"""
+        Return the Auslander-Reiten quiver of ``self``.
+
+        .. SEEALSO::
+
+            :class:`~sage.quivers.ar_quiver.AuslanderReitenQuiver`
+
+        EXAMPLES::
+
+            sage: D = DiGraph([[1,2,'a'], [1,2,'b']], multiedges=True)
+            sage: D.auslander_reiten_quiver()
+            Auslander-Reiten quiver of Multi-digraph on 2 vertices
+        """
+        from sage.quivers.ar_quiver import AuslanderReitenQuiver
+        return AuslanderReitenQuiver(self)
+
     # Directed Acyclic Graphs (DAGs)
 
     def topological_sort(self, implementation="default"):