mjo/clan/clan_element.py: composite det example for the Vinberg clan

diff --git a/mjo/clan/clan_element.py b/mjo/clan/clan_element.py
index bd481eaa3ba63d66f0e64e5c9e4db52604779ba6..eedf4815ea37522d878e761a7fbadb037f8bd166 100644 (file)
--- a/mjo/clan/clan_element.py
+++ b/mjo/clan/clan_element.py
@@ -260,7 +260,7 @@ class NormalDecompositionElement(ClanElement):
 
         SETUP::
 
-            sage: from mjo.clan.unital_clan import SnClan
+            sage: from mjo.clan.unital_clan import SnClan, VinbergClan
 
         EXAMPLES:
 
@@ -291,6 +291,24 @@ class NormalDecompositionElement(ClanElement):
             sage: phi(X).D(2)
             8
 
+        In the Vinberg clan (Ishi, p. 169) we see that the composite
+        determinant is the product of the determinants of the two
+        matrices that make up an element. Our results agree with
+        that::
+
+            sage: C = VinbergClan()
+            sage: A = matrix(QQ, [ [2, 1],
+            ....:                  [1, 4] ])
+            sage: B = matrix(QQ, [ [2, 2],
+            ....:                  [2,-1] ])
+            sage: A.det()
+            7
+            sage: B.det()
+            -6
+            sage: x = C.from_matrices(A, B)
+            sage: x.D(C.rank() - 1)
+            -42
+
         """
         # The sum() hijinks avoid needing to know what the third
         # coordinate is.