eja: implement element powers in terms of operator().

[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 5f9d5ba22435bb4c0de7391b35f18bc4d00d53fd..f913030a7a52be7d369a78ba026848dd986acade 100644 (file)
--- a/mjo/eja/euclidean_jordan_algebra.py
+++ b/mjo/eja/euclidean_jordan_algebra.py
@@ -761,7 +761,7 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
 
                 sage: set_random_seed()
                 sage: x = random_eja().random_element()
-                sage: x.operator_matrix()*x.vector() == (x^2).vector()
+                sage: x.operator()(x) == (x^2)
                 True
 
             A few examples of power-associativity::
@@ -780,19 +780,18 @@ 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).operator_matrix()
-                sage: Lxn = (x^n).operator_matrix()
+                sage: Lxm = (x^m).operator()
+                sage: Lxn = (x^n).operator()
                 sage: Lxm*Lxn == Lxn*Lxm
                 True
 
             """
-            A = self.parent()
             if n == 0:
-                return A.one()
+                return self.parent().one()
             elif n == 1:
                 return self
             else:
-                return A( (self.operator_matrix()**(n-1))*self.vector() )
+                return (self.operator()**(n-1))(self)
 
 
         def apply_univariate_polynomial(self, p):
@@ -967,8 +966,8 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
             if not other in self.parent():
                 raise TypeError("'other' must live in the same algebra")
 
-            A = self.operator_matrix()
-            B = other.operator_matrix()
+            A = self.operator()
+            B = other.operator()
             return (A*B == B*A)