+ sage: J = RealSymmetricEJA(2)
+ sage: id = identity_matrix(J.base_ring(), J.dimension())
+ sage: f = FiniteDimensionalEuclideanJordanAlgebraOperator(J,J,id)
+ sage: f^0 + f^1 + f^2
+ Linear operator between finite-dimensional Euclidean Jordan
+ algebras represented by the matrix:
+ [3 0 0]
+ [0 3 0]
+ [0 0 3]
+ Domain: Euclidean Jordan algebra of degree 3 over Rational Field
+ Codomain: Euclidean Jordan algebra of degree 3 over Rational Field
+
+ """
+ if (n == 1):
+ return self
+ elif (n == 0):
+ # Raising a vector space morphism to the zero power gives
+ # you back a special IdentityMorphism that is useless to us.
+ rows = self.codomain().dimension()
+ cols = self.domain().dimension()
+ mat = matrix.identity(self.base_ring(), rows, cols)
+ else:
+ mat = self.matrix()**n
+
+ return FiniteDimensionalEuclideanJordanAlgebraOperator(
+ self.domain(),
+ self.codomain(),
+ mat)
+
+
+ def _repr_(self):
+ r"""
+
+ A text representation of this linear operator on a Euclidean
+ Jordan Algebra.
+
+ EXAMPLES::
+
+ sage: J = JordanSpinEJA(2)
+ sage: id = identity_matrix(J.base_ring(), J.dimension())
+ sage: FiniteDimensionalEuclideanJordanAlgebraOperator(J,J,id)
+ Linear operator between finite-dimensional Euclidean Jordan
+ algebras represented by the matrix:
+ [1 0]
+ [0 1]
+ Domain: Euclidean Jordan algebra of degree 2 over Rational Field
+ Codomain: Euclidean Jordan algebra of degree 2 over Rational Field
+
+ """
+ msg = ("Linear operator between finite-dimensional Euclidean Jordan "
+ "algebras represented by the matrix:\n",
+ "{!r}\n",
+ "Domain: {}\n",
+ "Codomain: {}")
+ return ''.join(msg).format(self.matrix(),
+ self.domain(),
+ self.codomain())
+
+
+ def _sub_(self, other):
+ """
+ Subtract ``other`` from this EJA operator.
+
+ EXAMPLES::
+
+ sage: J = RealSymmetricEJA(2)
+ sage: id = identity_matrix(J.base_ring(),J.dimension())
+ sage: f = FiniteDimensionalEuclideanJordanAlgebraOperator(J,J,id)
+ sage: f - (f*2)
+ Linear operator between finite-dimensional Euclidean Jordan
+ algebras represented by the matrix:
+ [-1 0 0]
+ [ 0 -1 0]
+ [ 0 0 -1]
+ Domain: Euclidean Jordan algebra of degree 3 over Rational Field
+ Codomain: Euclidean Jordan algebra of degree 3 over Rational Field