X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_operator.py;h=0b52f555d51f58341fe56f5b63984f88cdf99da0;hb=4c6ab92d378613a9a053b62382b7e0cda7c450ab;hp=468a921fc2788176a696f93a9e042a5333a199e7;hpb=1ba4748f125c32d51ed1b3b89188f34546c9136f;p=sage.d.git

diff --git a/mjo/eja/eja_operator.py b/mjo/eja/eja_operator.py
index 468a921..0b52f55 100644
--- a/mjo/eja/eja_operator.py
+++ b/mjo/eja/eja_operator.py
@@ -419,6 +419,73 @@ class FiniteDimensionalEuclideanJordanAlgebraOperator(Map):
         return (self + (-other))
 
 
+    def is_self_adjoint(self):
+        r"""
+        Return whether or not this operator is self-adjoint.
+
+        At least in Sage, the fact that the base field is real means
+        that the algebra elements have to be real as well (this is why
+        we embed the complex numbers and quaternions). As a result, the
+        matrix of this operator will contain only real entries, and it
+        suffices to check only symmetry, not conjugate symmetry.
+
+        SETUP::
+
+            sage: from mjo.eja.eja_algebra import (JordanSpinEJA)
+
+        EXAMPLES::
+
+            sage: J = JordanSpinEJA(4)
+            sage: J.one().operator().is_self_adjoint()
+            True
+
+        """
+        return self.matrix().is_symmetric()
+
+
+    def is_zero(self):
+        r"""
+        Return whether or not this map is the zero operator.
+
+        SETUP::
+
+            sage: from mjo.eja.eja_operator import FiniteDimensionalEuclideanJordanAlgebraOperator
+            sage: from mjo.eja.eja_algebra import (random_eja,
+            ....:                                  JordanSpinEJA,
+            ....:                                  RealSymmetricEJA)
+
+        EXAMPLES::
+
+            sage: J1 = JordanSpinEJA(2)
+            sage: J2 = RealSymmetricEJA(2)
+            sage: R = J1.base_ring()
+            sage: M = matrix(R, [ [0, 0],
+            ....:                 [0, 0],
+            ....:                 [0, 0] ])
+            sage: L = FiniteDimensionalEuclideanJordanAlgebraOperator(J1,J2,M)
+            sage: L.is_zero()
+            True
+            sage: M = matrix(R, [ [0, 0],
+            ....:                 [0, 1],
+            ....:                 [0, 0] ])
+            sage: L = FiniteDimensionalEuclideanJordanAlgebraOperator(J1,J2,M)
+            sage: L.is_zero()
+            False
+
+        TESTS:
+
+        The left-multiplication-by-zero operation on a given algebra
+        is its zero map::
+
+            sage: set_random_seed()
+            sage: J = random_eja()
+            sage: J.zero().operator().is_zero()
+            True
+
+        """
+        return self.matrix().is_zero()
+
+
     def inverse(self):
         """
         Return the inverse of this operator, if it exists.