X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_algebra.py;h=04929467d114dbb23cc4fcc15f11c80df58addf0;hb=0d2f419ecd30a2d7899a37ab38ae6b4ff0e3245e;hp=bcafe57cbebd2b974eda6e3f13b3ceda26ffd4ab;hpb=9ef0028e6f5d1748f1d24214ad1cccc686edfa54;p=sage.d.git

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index bcafe57..0492946 100644
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -993,7 +993,24 @@ class MatrixEuclideanJordanAlgebra(FiniteDimensionalEuclideanJordanAlgebra):
             J = MatrixEuclideanJordanAlgebra(QQ,
                                              basis,
                                              normalize_basis=False)
-            return J._charpoly_coefficients()
+            a = J._charpoly_coefficients()
+
+            # Unfortunately, changing the basis does change the
+            # coefficients of the characteristic polynomial, but since
+            # these are really the coefficients of the "characteristic
+            # polynomial of" function, everything is still nice and
+            # unevaluated. It's therefore "obvious" how scaling the
+            # basis affects the coordinate variables X1, X2, et
+            # cetera. Scaling the first basis vector up by "n" adds a
+            # factor of 1/n into every "X1" term, for example. So here
+            # we simply undo the basis_normalizer scaling that we
+            # performed earlier.
+            #
+            # TODO: make this access safe.
+            XS = a[0].variables()
+            subs_dict = { XS[i]: self._basis_normalizers[i]*XS[i]
+                          for i in range(len(XS)) }
+            return tuple( a_i.subs(subs_dict) for a_i in a )
 
 
     @staticmethod
@@ -1011,6 +1028,9 @@ class MatrixEuclideanJordanAlgebra(FiniteDimensionalEuclideanJordanAlgebra):
         # is supposed to hold the entire long vector, and the subspace W
         # of V will be spanned by the vectors that arise from symmetric
         # matrices. Thus for S^2, dim(V) == 4 and dim(W) == 3.
+        if len(basis) == 0:
+            return []
+
         field = basis[0].base_ring()
         dimension = basis[0].nrows()
 
@@ -1168,6 +1188,11 @@ class RealSymmetricEJA(RealMatrixEuclideanJordanAlgebra):
         sage: x.operator().matrix().is_symmetric()
         True
 
+    We can construct the (trivial) algebra of rank zero::
+
+        sage: RealSymmetricEJA(0)
+        Euclidean Jordan algebra of dimension 0 over Algebraic Real Field
+
     """
     @classmethod
     def _denormalized_basis(cls, n, field):
@@ -1441,6 +1466,11 @@ class ComplexHermitianEJA(ComplexMatrixEuclideanJordanAlgebra):
         sage: x.operator().matrix().is_symmetric()
         True
 
+    We can construct the (trivial) algebra of rank zero::
+
+        sage: ComplexHermitianEJA(0)
+        Euclidean Jordan algebra of dimension 0 over Algebraic Real Field
+
     """
 
     @classmethod
@@ -1736,6 +1766,11 @@ class QuaternionHermitianEJA(QuaternionMatrixEuclideanJordanAlgebra):
         sage: x.operator().matrix().is_symmetric()
         True
 
+    We can construct the (trivial) algebra of rank zero::
+
+        sage: QuaternionHermitianEJA(0)
+        Euclidean Jordan algebra of dimension 0 over Algebraic Real Field
+
     """
     @classmethod
     def _denormalized_basis(cls, n, field):