eja: add algebra constructors to the global namespace.

[sage.d.git] / mjo / eja / euclidean_jordan_algebra.py

diff --git a/mjo/eja/euclidean_jordan_algebra.py b/mjo/eja/euclidean_jordan_algebra.py
index ba2c63cf492a663dcb252ef5f49fa5b6f68e6c88..70a77701b342e36eec827d3ec151b87bf67fe902 100644 (file)
--- a/mjo/eja/euclidean_jordan_algebra.py
+++ b/mjo/eja/euclidean_jordan_algebra.py
@@ -146,6 +146,7 @@ class FiniteDimensionalEuclideanJordanAlgebraOperator(Map):
             return False
         return True
 
+
     def __invert__(self):
         """
         Invert this EJA operator.
@@ -351,6 +352,22 @@ class FiniteDimensionalEuclideanJordanAlgebraOperator(Map):
         return self._matrix
 
 
+    def minimal_polynomial(self):
+        """
+        Return the minimal polynomial of this linear operator,
+        in the variable ``t``.
+
+        EXAMPLES::
+
+            sage: J = RealSymmetricEJA(3)
+            sage: J.one().operator().minimal_polynomial()
+            t - 1
+
+        """
+        # The matrix method returns a polynomial in 'x' but want one in 't'.
+        return self.matrix().minimal_polynomial().change_variable_name('t')
+
+
 class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
     @staticmethod
     def __classcall_private__(cls,
@@ -1349,11 +1366,8 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
             # and subalgebra_generated_by() must be the same, and in
             # the same order!
             elt = assoc_subalg(V.coordinates(self.vector()))
+            return elt.operator().minimal_polynomial()
 
-            # We get back a symbolic polynomial in 'x' but want a real
-            # polynomial in 't'.
-            p_of_x = elt.operator_matrix().minimal_polynomial()
-            return p_of_x.change_variable_name('t')
 
 
         def natural_representation(self):
@@ -1422,34 +1436,11 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
 
             """
             P = self.parent()
+            fda_elt = FiniteDimensionalAlgebraElement(P, self)
             return FiniteDimensionalEuclideanJordanAlgebraOperator(
-                     P,P,
-                     self.operator_matrix() )
-
-
-
-        def operator_matrix(self):
-            """
-            Return the matrix that represents left- (or right-)
-            multiplication by this element in the parent algebra.
-
-            We implement this ourselves to work around the fact that
-            our parent class represents everything with row vectors.
-
-            EXAMPLES:
-
-            Ensure that our operator's ``matrix`` method agrees with
-            this implementation::
-
-                sage: set_random_seed()
-                sage: J = random_eja()
-                sage: x = J.random_element()
-                sage: x.operator().matrix() == x.operator_matrix()
-                True
-
-            """
-            fda_elt = FiniteDimensionalAlgebraElement(self.parent(), self)
-            return fda_elt.matrix().transpose()
+                     P,
+                     P,
+                     fda_elt.matrix().transpose() )
 
 
         def quadratic_representation(self, other=None):
@@ -1671,7 +1662,7 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
             s = 0
             minimal_dim = V.dimension()
             for i in xrange(1, V.dimension()):
-                this_dim = (u**i).operator_matrix().image().dimension()
+                this_dim = (u**i).operator().matrix().image().dimension()
                 if this_dim < minimal_dim:
                     minimal_dim = this_dim
                     s = i
@@ -1688,7 +1679,7 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
             # Beware, solve_right() means that we're using COLUMN vectors.
             # Our FiniteDimensionalAlgebraElement superclass uses rows.
             u_next = u**(s+1)
-            A = u_next.operator_matrix()
+            A = u_next.operator().matrix()
             c_coordinates = A.solve_right(u_next.vector())
 
             # Now c_coordinates is the idempotent we want, but it's in