mjo/clan/jordan_spin_clan.py: fix the clan product

I forgot a "2", and now that it's there we can verify the homogeneous
polynomials D(0) and D(1).

diff --git a/mjo/clan/jordan_spin_clan.py b/mjo/clan/jordan_spin_clan.py
index 12282f96362c934ae728bf34104ce2a479f874c6..5d836d046fd58e0020290b0f15dc45907ed2809e 100644 (file)
--- a/mjo/clan/jordan_spin_clan.py
+++ b/mjo/clan/jordan_spin_clan.py
@@ -18,6 +18,21 @@ class JordanSpinClan(NormalDecomposition):
 
         sage: from mjo.clan.jordan_spin_clan import JordanSpinClan
 
+    EXAMPLES:
+
+    The ``D`` polynomials for this clan are given by Gindikin on page
+    90. We verify them for one example::
+
+        sage: C = JordanSpinClan(7)
+        sage: x = C.from_vector(vector(QQ,[1,2,3,4,5,6,7]))
+        sage: x21 = x.to_vector()[1:-1]
+        sage: x22 = x.to_vector()[-1]
+        sage: x11 = x.to_vector()[0]
+        sage: x.D(0) == x11
+        True
+        sage: x.D(1) == x11*x22 - x21.inner_product(x21)
+        True
+
     TESTS:
 
     Verifying the axioms::
@@ -82,7 +97,7 @@ class JordanSpinClan(NormalDecomposition):
             V = x.parent()
             z11 = x11*y11
             z21 = y_bar*(x11 + x22)/two + y11*x_bar
-            z22 = x22*y22 + x_bar.inner_product(y_bar)
+            z22 = x22*y22 + 2*x_bar.inner_product(y_bar)
             z_coords = [z11] + list(z21) + [z22]
             return RN.from_vector(V(z_coords))