eja: add is_self_adjoint() for operators.

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

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index 21718ee85e168d9ead63b061a3d623cb3ab6c8cc..2ea1a9267623d95d02231654a48a470efc186a40 100644 (file)
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -24,15 +24,12 @@ from sage.combinat.free_module import CombinatorialFreeModule
 from sage.matrix.constructor import matrix
 from sage.matrix.matrix_space import MatrixSpace
 from sage.misc.cachefunc import cached_method
-from sage.misc.lazy_import import lazy_import
 from sage.misc.table import table
 from sage.modules.free_module import FreeModule, VectorSpace
 from sage.rings.all import (ZZ, QQ, AA, QQbar, RR, RLF, CLF,
                             PolynomialRing,
                             QuadraticField)
 from mjo.eja.eja_element import FiniteDimensionalEuclideanJordanAlgebraElement
-lazy_import('mjo.eja.eja_subalgebra',
-            'FiniteDimensionalEuclideanJordanSubalgebra')
 from mjo.eja.eja_operator import FiniteDimensionalEuclideanJordanAlgebraOperator
 from mjo.eja.eja_utils import _mat2vec
 
@@ -57,7 +54,7 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule):
             sage: J(1)
             Traceback (most recent call last):
             ...
-            ValueError: not a naturally-represented algebra element
+            ValueError: not an element of this algebra
 
         """
         return None
@@ -180,7 +177,7 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule):
             sage: J(A)
             Traceback (most recent call last):
             ...
-            ArithmeticError: vector is not in free module
+            ValueError: not an element of this algebra
 
         TESTS:
 
@@ -199,7 +196,7 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule):
             True
 
         """
-        msg = "not a naturally-represented algebra element"
+        msg = "not an element of this algebra"
         if elt == 0:
             # The superclass implementation of random_element()
             # needs to be able to coerce "0" into the algebra.
@@ -224,7 +221,12 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule):
         # could be QQ instead of QQbar.
         V = VectorSpace(basis_space.base_ring(), elt.nrows()*elt.ncols())
         W = V.span_of_basis( _mat2vec(s) for s in natural_basis )
-        coords =  W.coordinate_vector(_mat2vec(elt))
+
+        try:
+            coords =  W.coordinate_vector(_mat2vec(elt))
+        except ArithmeticError:  # vector is not in free module
+            raise ValueError(msg)
+
         return self.from_vector(coords)
 
     def _repr_(self):
@@ -768,6 +770,8 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule):
         if not c.is_idempotent():
             raise ValueError("element is not idempotent: %s" % c)
 
+        from mjo.eja.eja_subalgebra import FiniteDimensionalEuclideanJordanSubalgebra
+
         # Default these to what they should be if they turn out to be
         # trivial, because eigenspaces_left() won't return eigenvalues
         # corresponding to trivial spaces (e.g. it returns only the
@@ -1119,7 +1123,7 @@ class ConcreteEuclideanJordanAlgebra:
         sage: set_random_seed()
         sage: J = ConcreteEuclideanJordanAlgebra.random_instance()
         sage: x = J.random_element()
-        sage: x.operator().matrix().is_symmetric()
+        sage: x.operator().is_self_adjoint()
         True
 
     """