eja: add is_self_adjoint() for operators.

[sage.d.git] / mjo / eja / eja_operator.py

diff --git a/mjo/eja/eja_operator.py b/mjo/eja/eja_operator.py
index 2a0c9c48633cd06551c49515840680b57a5b927d..0b52f555d51f58341fe56f5b63984f88cdf99da0 100644 (file)
--- a/mjo/eja/eja_operator.py
+++ b/mjo/eja/eja_operator.py
@@ -3,12 +3,48 @@ from sage.categories.all import FreeModules
 from sage.categories.map import Map
 
 class FiniteDimensionalEuclideanJordanAlgebraOperator(Map):
+    r"""
+    An operator between two finite-dimensional Euclidean Jordan algebras.
+
+    SETUP::
+
+        sage: from mjo.eja.eja_algebra import HadamardEJA
+        sage: from mjo.eja.eja_operator import FiniteDimensionalEuclideanJordanAlgebraOperator
+
+    EXAMPLES:
+
+    The domain and codomain must be finite-dimensional Euclidean
+    Jordan algebras; if either is not, then an error is raised::
+
+        sage: J = HadamardEJA(3)
+        sage: V = VectorSpace(J.base_ring(), 3)
+        sage: M = matrix.identity(J.base_ring(), 3)
+        sage: FiniteDimensionalEuclideanJordanAlgebraOperator(V,J,M)
+        Traceback (most recent call last):
+        ...
+        TypeError: domain must be a finite-dimensional Euclidean
+        Jordan algebra
+        sage: FiniteDimensionalEuclideanJordanAlgebraOperator(J,V,M)
+        Traceback (most recent call last):
+        ...
+        TypeError: codomain must be a finite-dimensional Euclidean
+        Jordan algebra
+
+    """
+
     def __init__(self, domain_eja, codomain_eja, mat):
-        # if not (
-        #   isinstance(domain_eja, FiniteDimensionalEuclideanJordanAlgebra) and
-        #   isinstance(codomain_eja, FiniteDimensionalEuclideanJordanAlgebra) ):
-        #     raise ValueError('(co)domains must be finite-dimensional Euclidean '
-        #                      'Jordan algebras')
+        from mjo.eja.eja_algebra import FiniteDimensionalEuclideanJordanAlgebra
+
+        # I guess we should check this, because otherwise you could
+        # pass in pretty much anything algebraish.
+        if not isinstance(domain_eja,
+                          FiniteDimensionalEuclideanJordanAlgebra):
+            raise TypeError('domain must be a finite-dimensional '
+                            'Euclidean Jordan algebra')
+        if not isinstance(codomain_eja,
+                          FiniteDimensionalEuclideanJordanAlgebra):
+            raise TypeError('codomain must be a finite-dimensional '
+                            'Euclidean Jordan algebra')
 
         F = domain_eja.base_ring()
         if not (F == codomain_eja.base_ring()):
@@ -117,17 +153,17 @@ class FiniteDimensionalEuclideanJordanAlgebraOperator(Map):
             sage: from mjo.eja.eja_operator import FiniteDimensionalEuclideanJordanAlgebraOperator
             sage: from mjo.eja.eja_algebra import (
             ....:   JordanSpinEJA,
-            ....:   RealCartesianProductEJA,
+            ....:   HadamardEJA,
             ....:   RealSymmetricEJA)
 
         EXAMPLES::
 
             sage: J1 = JordanSpinEJA(3)
-            sage: J2 = RealCartesianProductEJA(2)
+            sage: J2 = HadamardEJA(2)
             sage: J3 = RealSymmetricEJA(1)
-            sage: mat1 = matrix(QQ, [[1,2,3],
+            sage: mat1 = matrix(AA, [[1,2,3],
             ....:                    [4,5,6]])
-            sage: mat2 = matrix(QQ, [[7,8]])
+            sage: mat2 = matrix(AA, [[7,8]])
             sage: g = FiniteDimensionalEuclideanJordanAlgebraOperator(J1,
             ....:                                                     J2,
             ....:                                                     mat1)
@@ -139,9 +175,9 @@ class FiniteDimensionalEuclideanJordanAlgebraOperator(Map):
             algebras represented by the matrix:
             [39 54 69]
             Domain: Euclidean Jordan algebra of dimension 3 over
-            Rational Field
+            Algebraic Real Field
             Codomain: Euclidean Jordan algebra of dimension 1 over
-            Rational Field
+            Algebraic Real Field
 
         """
         return FiniteDimensionalEuclideanJordanAlgebraOperator(
@@ -341,9 +377,9 @@ class FiniteDimensionalEuclideanJordanAlgebraOperator(Map):
             [1 0]
             [0 1]
             Domain: Euclidean Jordan algebra of dimension 2 over
-            Rational Field
+            Algebraic Real Field
             Codomain: Euclidean Jordan algebra of dimension 2 over
-            Rational Field
+            Algebraic Real Field
 
         """
         msg = ("Linear operator between finite-dimensional Euclidean Jordan "
@@ -383,6 +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.
@@ -542,7 +645,7 @@ class FiniteDimensionalEuclideanJordanAlgebraOperator(Map):
 
         EXAMPLES::
 
-            sage: J = RealSymmetricEJA(4,AA)
+            sage: J = RealSymmetricEJA(4)
             sage: x = sum(J.gens())
             sage: A = x.subalgebra_generated_by(orthonormalize_basis=True)
             sage: L0x = A(x).operator()
@@ -582,4 +685,4 @@ class FiniteDimensionalEuclideanJordanAlgebraOperator(Map):
                    self.codomain(),
                    mat)
             projectors.append(Pi)
-        return zip(eigenvalues, projectors)
+        return list(zip(eigenvalues, projectors))