X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feuclidean_jordan_algebra.py;h=30d04f4a352b7d553470bd456d18d224e2ec5428;hb=31baec0eee0c53b0cfe379c744cdf174aa57ebd9;hp=713eca534b1028dadddf4bb6e99953de0d6b1cd0;hpb=f117a2240c2bb5e87cb82485db701a40d5dbad04;p=sage.d.git

diff --git a/mjo/eja/euclidean_jordan_algebra.py b/mjo/eja/euclidean_jordan_algebra.py
index 713eca5..30d04f4 100644
--- a/mjo/eja/euclidean_jordan_algebra.py
+++ b/mjo/eja/euclidean_jordan_algebra.py
@@ -81,6 +81,18 @@ class FiniteDimensionalEuclideanJordanAlgebraHomset(FiniteDimensionalAlgebraHoms
         return FiniteDimensionalEuclideanJordanAlgebraMorphism(self, x)
 
 
+    def one(self):
+        """
+        Return the identity morphism, but as a member of the right
+        space (so that we can add it, multiply it, etc.)
+        """
+        cols = self.domain().dimension()
+        rows = self.codomain().dimension()
+        mat = identity_matrix(self.base_ring(), rows, cols)
+        return FiniteDimensionalEuclideanJordanAlgebraMorphism(self, mat)
+
+
+
 class FiniteDimensionalEuclideanJordanAlgebraMorphism(FiniteDimensionalAlgebraMorphism):
     """
     A linear map between two finite-dimensional EJAs.
@@ -260,6 +272,37 @@ class FiniteDimensionalEuclideanJordanAlgebraMorphism(FiniteDimensionalAlgebraMo
     __mul__ = _lmul_
 
 
+    def __pow__(self, n):
+        """
+
+        TESTS::
+
+            sage: J = JordanSpinEJA(4)
+            sage: e0,e1,e2,e3 = J.gens()
+            sage: x = -5/2*e0 + 1/2*e2 + 20*e3
+            sage: Qx = x.quadratic_representation()
+            sage: Qx^0
+            Morphism from Euclidean Jordan algebra of degree 4 over Rational
+            Field to Euclidean Jordan algebra of degree 4 over Rational Field
+            given by matrix
+            [1 0 0 0]
+            [0 1 0 0]
+            [0 0 1 0]
+            [0 0 0 1]
+            sage: (x^0).quadratic_representation() == Qx^0
+            True
+
+        """
+        if n == 0:
+            # We get back the stupid identity morphism which doesn't
+            # live in the right space.
+            return self.parent().one()
+        elif n == 1:
+            return self
+        else:
+            return FiniteDimensionalAlgebraMorphism.__pow__(self,n)
+
+
     def _neg_(self):
         """
         Negate this morphism.
@@ -1041,12 +1084,12 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
                 sage: n = ZZ.random_element(1,10)
                 sage: J = JordanSpinEJA(n)
                 sage: x = J.random_element()
-                sage: while x.is_zero():
+                sage: while not x.is_invertible():
                 ....:     x = J.random_element()
                 sage: x_vec = x.vector()
                 sage: x0 = x_vec[0]
                 sage: x_bar = x_vec[1:]
-                sage: coeff = 1/(x0^2 - x_bar.inner_product(x_bar))
+                sage: coeff = ~(x0^2 - x_bar.inner_product(x_bar))
                 sage: inv_vec = x_vec.parent()([x0] + (-x_bar).list())
                 sage: x_inverse = coeff*inv_vec
                 sage: x.inverse() == J(x_inverse)