mjo/clan/unital_clan.py: factor out (un)lift for the Vinberg clan

diff --git a/mjo/clan/unital_clan.py b/mjo/clan/unital_clan.py
index 63fb737f47d99baf93e28c2a2815bdadba2faa08..c07404f87ad2514b4c1dd9467043f05e110d9b44 100644 (file)
--- a/mjo/clan/unital_clan.py
+++ b/mjo/clan/unital_clan.py
@@ -619,6 +619,24 @@ class VinbergClan(NormalDecomposition):
         True
 
     """
+    def _unlift(self, pair):
+        A,B = pair
+        R5 = self._vector_space
+        return ( A[(0,0,1)]*R5((0,0,1)) +
+                 A[(1,0,1)]*R5((1,0,1)) +
+                 A[(1,1,1)]*R5((1,1,1)) +
+                 B[(1,0,1)]*R5((2,0,1)) +
+                 B[(1,1,1)]*R5((2,2,1)) )
+
+    def _lift(self, v):
+        M1 = ( self._S2((0,0,1))*v[(0,0,1)] +
+               self._S2((1,0,1))*v[(1,0,1)] +
+               self._S2((1,1,1))*v[(1,1,1)] )
+        M2 = ( self._S2((0,0,1))*v[(0,0,1)] +
+               self._S2((1,0,1))*v[(2,0,1)] +
+               self._S2((1,1,1))*v[(2,2,1)] )
+        return (M1,M2)
+
     def __init__(self, scalar_field=QQ, **kwargs):
         from sage.matrix.matrix_space import MatrixSpace
         from sage.modules.free_module import VectorSpace
@@ -653,36 +671,24 @@ class VinbergClan(NormalDecomposition):
             (2,2,1)
         ])
 
-        def unlift(pair):
-            A,B = pair
-            return ( A[(0,0,1)]*R5((0,0,1)) +
-                     A[(1,0,1)]*R5((1,0,1)) +
-                     A[(1,1,1)]*R5((1,1,1)) +
-                     B[(1,0,1)]*R5((2,0,1)) +
-                     B[(1,1,1)]*R5((2,2,1)) )
-
-        def lift(v):
-            M1 = ( self._S2((0,0,1))*v[(0,0,1)] +
-                   self._S2((1,0,1))*v[(1,0,1)] +
-                   self._S2((1,1,1))*v[(1,1,1)] )
-            M2 = ( self._S2((0,0,1))*v[(0,0,1)] +
-                   self._S2((1,0,1))*v[(2,0,1)] +
-                   self._S2((1,1,1))*v[(2,2,1)] )
-            return (M1,M2)
+        # The Clan __init__ does this, but if we do it now then we can
+        # use the self.lift() and self.unlift() methods to define the
+        # clan product rather than duplicating them locally.
+        self._vector_space = R5
 
         def cp(x,y):
             # up_hat and down_hat need MatrixSpace elements, not
             # submodules with custom bases, so we need to lift
             # everything twice.
-            X1,X2 = lift(x)
-            Y1,Y2 = lift(y)
+            X1,X2 = self._lift(x)
+            Y1,Y2 = self._lift(y)
             X1 = X1.lift()
             X2 = X2.lift()
             Y1 = Y1.lift()
             Y2 = Y2.lift()
             Z1 = MatrixClan._down_hat(X1)*Y1 + Y1*MatrixClan._up_hat(X1)
             Z2 = MatrixClan._down_hat(X2)*Y2 + Y2*MatrixClan._up_hat(X2)
-            return unlift((self._S2(Z1), self._S2(Z2)))
+            return self._unlift((self._S2(Z1), self._S2(Z2)))
 
         def ip(x,y):
             two = x.base_ring()(2)