X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feuclidean_jordan_algebra.py;h=da3f6001e2d3878f6c5311eb309f8b2a22676a00;hb=9b6acc401eb02e9565db6212698662c9844c4239;hp=a469bb0d7ba1302ccf30289c9b1c0c5518ed527f;hpb=8f7ecef93d07a3f969d1c944c80b75a7052a4975;p=sage.d.git

diff --git a/mjo/eja/euclidean_jordan_algebra.py b/mjo/eja/euclidean_jordan_algebra.py
index a469bb0..da3f600 100644
--- a/mjo/eja/euclidean_jordan_algebra.py
+++ b/mjo/eja/euclidean_jordan_algebra.py
@@ -1086,38 +1086,77 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
                 sage: J = random_eja()
                 sage: x = J.random_element()
                 sage: y = J.random_element()
+                sage: Lx = x.operator_matrix()
+                sage: Lxx = (x*x).operator_matrix()
+                sage: Qx = x.quadratic_representation()
+                sage: Qy = y.quadratic_representation()
+                sage: Qxy = x.quadratic_representation(y)
+                sage: Qex = J.one().quadratic_representation(x)
+                sage: n = ZZ.random_element(10)
+                sage: Qxn = (x^n).quadratic_representation()
 
             Property 1:
 
-                sage: actual = x.quadratic_representation(y)
-                sage: expected = ( (x+y).quadratic_representation()
-                ....:              -x.quadratic_representation()
-                ....:              -y.quadratic_representation() ) / 2
-                sage: actual == expected
+                sage: 2*Qxy == (x+y).quadratic_representation() - Qx - Qy
                 True
 
             Property 2:
 
                 sage: alpha = QQ.random_element()
-                sage: actual = (alpha*x).quadratic_representation()
-                sage: expected = (alpha^2)*x.quadratic_representation()
-                sage: actual == expected
+                sage: (alpha*x).quadratic_representation() == (alpha^2)*Qx
+                True
+
+            Property 3:
+
+                sage: not x.is_invertible() or (
+                ....:     Qx*x.inverse().vector() == x.vector() )
+                True
+
+                sage: not x.is_invertible() or (
+                ....:   Qx.inverse()
+                ....:   ==
+                ....:   x.inverse().quadratic_representation() )
+                True
+
+                sage: Qxy*(J.one().vector()) == (x*y).vector()
+                True
+
+            Property 4:
+
+                sage: not x.is_invertible() or (
+                ....:   x.quadratic_representation(x.inverse())*Qx
+                ....:   == Qx*x.quadratic_representation(x.inverse()) )
+                True
+
+                sage: not x.is_invertible() or (
+                ....:   x.quadratic_representation(x.inverse())*Qx
+                ....:   ==
+                ....:   2*x.operator_matrix()*Qex - Qx )
+                True
+
+                sage: 2*x.operator_matrix()*Qex - Qx == Lxx
                 True
 
             Property 5:
 
-                sage: Qy = y.quadratic_representation()
-                sage: actual = J(Qy*x.vector()).quadratic_representation()
-                sage: expected = Qy*x.quadratic_representation()*Qy
-                sage: actual == expected
+                sage: J(Qy*x.vector()).quadratic_representation() == Qy*Qx*Qy
                 True
 
             Property 6:
 
-                sage: k = ZZ.random_element(1,10)
-                sage: actual = (x^k).quadratic_representation()
-                sage: expected = (x.quadratic_representation())^k
-                sage: actual == expected
+                sage: Qxn == (Qx)^n
+                True
+
+            Property 7:
+
+                sage: not x.is_invertible() or (
+                ....:   Qx*x.inverse().operator_matrix() == Lx )
+                True
+
+            Property 8:
+
+                sage: not x.operator_commutes_with(y) or (
+                ....:   J(Qx*y.vector())^n == J(Qxn*(y^n).vector()) )
                 True
 
             """
@@ -1211,12 +1250,11 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
             TESTS::
 
                 sage: set_random_seed()
-                sage: J = RealCartesianProductEJA(5)
-                sage: c = J.random_element().subalgebra_idempotent()
-                sage: c^2 == c
-                True
-                sage: J = JordanSpinEJA(5)
-                sage: c = J.random_element().subalgebra_idempotent()
+                sage: J = random_eja()
+                sage: x = J.random_element()
+                sage: while x.is_nilpotent():
+                ....:     x = J.random_element()
+                sage: c = x.subalgebra_idempotent()
                 sage: c^2 == c
                 True