eja: factor out mat2vec() and vec2mat() helper functions.

diff --git a/mjo/eja/euclidean_jordan_algebra.py b/mjo/eja/euclidean_jordan_algebra.py
index a73cfaf689c7206f7644e10021006e4bcf6f08f7..e30c34128b564499d0485c3d0f9fcb68a826e6c7 100644 (file)
--- a/mjo/eja/euclidean_jordan_algebra.py
+++ b/mjo/eja/euclidean_jordan_algebra.py
@@ -1057,6 +1057,12 @@ def _complex_hermitian_basis(n, field=QQ):
     return tuple(S)
 
 
+def _mat2vec(m):
+        return vector(m.base_ring(), m.list())
+
+def _vec2mat(v):
+        return matrix(v.base_ring(), sqrt(v.degree()), v.list())
+
 def _multiplication_table_from_matrix_basis(basis):
     """
     At least three of the five simple Euclidean Jordan algebras have the
@@ -1077,19 +1083,13 @@ def _multiplication_table_from_matrix_basis(basis):
     field = basis[0].base_ring()
     dimension = basis[0].nrows()
 
-    def mat2vec(m):
-        return vector(field, m.list())
-
-    def vec2mat(v):
-        return matrix(field, dimension, v.list())
-
     V = VectorSpace(field, dimension**2)
-    W = V.span( mat2vec(s) for s in basis )
+    W = V.span( _mat2vec(s) for s in basis )
 
     # Taking the span above reorders our basis (thanks, jerk!) so we
     # need to put our "matrix basis" in the same order as the
     # (reordered) vector basis.
-    S = tuple( vec2mat(b) for b in W.basis() )
+    S = tuple( _vec2mat(b) for b in W.basis() )
 
     Qs = []
     for s in S:
@@ -1102,7 +1102,7 @@ def _multiplication_table_from_matrix_basis(basis):
         # why we're computing rows here and not columns.
         Q_rows = []
         for t in S:
-            this_row = mat2vec((s*t + t*s)/2)
+            this_row = _mat2vec((s*t + t*s)/2)
             Q_rows.append(W.coordinates(this_row))
         Q = matrix(field, W.dimension(), Q_rows)
         Qs.append(Q)