eja: define operator_matrix() to eventually replace matrix().

diff --git a/mjo/eja/euclidean_jordan_algebra.py b/mjo/eja/euclidean_jordan_algebra.py
index 4713ff0859876b5832e6e5e9551f632444c6a138..c0b7787a535b7754c446fcb0046c300b21695579 100644 (file)
--- a/mjo/eja/euclidean_jordan_algebra.py
+++ b/mjo/eja/euclidean_jordan_algebra.py
@@ -112,7 +112,7 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
 
                 sage: set_random_seed()
                 sage: x = random_eja().random_element()
-                sage: x.matrix()*x.vector() == (x^2).vector()
+                sage: x.operator_matrix()*x.vector() == (x^2).vector()
                 True
 
             A few examples of power-associativity::
@@ -131,8 +131,8 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
                 sage: x = random_eja().random_element()
                 sage: m = ZZ.random_element(0,10)
                 sage: n = ZZ.random_element(0,10)
-                sage: Lxm = (x^m).matrix()
-                sage: Lxn = (x^n).matrix()
+                sage: Lxm = (x^m).operator_matrix()
+                sage: Lxn = (x^n).operator_matrix()
                 sage: Lxm*Lxn == Lxn*Lxm
                 True
 
@@ -143,7 +143,7 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
             elif n == 1:
                 return self
             else:
-                return A.element_class(A, (self.matrix()**(n-1))*self.vector())
+                return A( (self.operator_matrix()**(n-1))*self.vector() )
 
 
         def characteristic_polynomial(self):
@@ -193,8 +193,8 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
             if not other in self.parent():
                 raise ArgumentError("'other' must live in the same algebra")
 
-            A = self.matrix()
-            B = other.matrix()
+            A = self.operator_matrix()
+            B = other.operator_matrix()
             return (A*B == B*A)
 
 
@@ -432,10 +432,10 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
                 sage: J = random_eja()
                 sage: x = J.random_element()
                 sage: y = J.random_element()
-                sage: Lx = x.matrix()
-                sage: Ly = y.matrix()
-                sage: Lxx = (x*x).matrix()
-                sage: Lxy = (x*y).matrix()
+                sage: Lx = x.operator_matrix()
+                sage: Ly = y.operator_matrix()
+                sage: Lxx = (x*x).operator_matrix()
+                sage: Lxy = (x*y).operator_matrix()
                 sage: bool(2*Lx*Lxy + Ly*Lxx == 2*Lxy*Lx + Lxx*Ly)
                 True
 
@@ -447,12 +447,12 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
                 sage: x = J.random_element()
                 sage: y = J.random_element()
                 sage: z = J.random_element()
-                sage: Lx = x.matrix()
-                sage: Ly = y.matrix()
-                sage: Lz = z.matrix()
-                sage: Lzy = (z*y).matrix()
-                sage: Lxy = (x*y).matrix()
-                sage: Lxz = (x*z).matrix()
+                sage: Lx = x.operator_matrix()
+                sage: Ly = y.operator_matrix()
+                sage: Lz = z.operator_matrix()
+                sage: Lzy = (z*y).operator_matrix()
+                sage: Lxy = (x*y).operator_matrix()
+                sage: Lxz = (x*z).operator_matrix()
                 sage: bool(Lx*Lzy + Lz*Lxy + Ly*Lxz == Lzy*Lx + Lxy*Lz + Lxz*Ly)
                 True
 
@@ -464,13 +464,13 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
                 sage: u = J.random_element()
                 sage: y = J.random_element()
                 sage: z = J.random_element()
-                sage: Lu = u.matrix()
-                sage: Ly = y.matrix()
-                sage: Lz = z.matrix()
-                sage: Lzy = (z*y).matrix()
-                sage: Luy = (u*y).matrix()
-                sage: Luz = (u*z).matrix()
-                sage: Luyz = (u*(y*z)).matrix()
+                sage: Lu = u.operator_matrix()
+                sage: Ly = y.operator_matrix()
+                sage: Lz = z.operator_matrix()
+                sage: Lzy = (z*y).operator_matrix()
+                sage: Luy = (u*y).operator_matrix()
+                sage: Luz = (u*z).operator_matrix()
+                sage: Luyz = (u*(y*z)).operator_matrix()
                 sage: lhs = Lu*Lzy + Lz*Luy + Ly*Luz
                 sage: rhs = Luyz + Ly*Lu*Lz + Lz*Lu*Ly
                 sage: bool(lhs == rhs)
@@ -480,6 +480,14 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
             fda_elt = FiniteDimensionalAlgebraElement(self.parent(), self)
             return fda_elt.matrix().transpose()
 
+        #
+        # The plan is to eventually phase out "matrix()", which sounds
+        # too much like "matrix_representation()", in favor of the more-
+        # accurate "operator_matrix()". But we need to override matrix()
+        # to keep parent class methods happy in the meantime.
+        #
+        operator_matrix = matrix
+
 
         def minimal_polynomial(self):
             """
@@ -610,9 +618,9 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
             elif not other in self.parent():
                 raise ArgumentError("'other' must live in the same algebra")
 
-            return ( self.matrix()*other.matrix()
-                       + other.matrix()*self.matrix()
-                       - (self*other).matrix() )
+            L = self.operator_matrix()
+            M = other.operator_matrix()
+            return ( L*M + M*L - (self*other).operator_matrix() )
 
 
         def span_of_powers(self):
@@ -645,7 +653,7 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
                 sage: set_random_seed()
                 sage: x = random_eja().random_element()
                 sage: u = x.subalgebra_generated_by().random_element()
-                sage: u.matrix()*u.vector() == (u**2).vector()
+                sage: u.operator_matrix()*u.vector() == (u**2).vector()
                 True
 
             """
@@ -717,7 +725,7 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
             s = 0
             minimal_dim = V.dimension()
             for i in xrange(1, V.dimension()):
-                this_dim = (u**i).matrix().image().dimension()
+                this_dim = (u**i).operator_matrix().image().dimension()
                 if this_dim < minimal_dim:
                     minimal_dim = this_dim
                     s = i
@@ -734,7 +742,7 @@ 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.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