X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_algebra.py;h=a0af3f0ef543dd951b2463a8aef0f295a2561287;hb=efe6cd067e02b788bfcdc5e8b61e994cd524120c;hp=c569098b3d3e5d6fbceef6352e22861dd125a7f8;hpb=af79c1d027cf737d125b11fd41bb0bc2150778fb;p=sage.d.git

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index c569098..a0af3f0 100644
--- 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):
@@ -374,6 +376,28 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule):
 
         return (t**r + sum( a[k]*(t**k) for k in range(r) ))
 
+    def coordinate_polynomial_ring(self):
+        r"""
+        The multivariate polynomial ring in which this algebra's
+        :meth:`characteristic_polynomial_of` lives.
+
+        SETUP::
+
+            sage: from mjo.eja.eja_algebra import (HadamardEJA,
+            ....:                                  RealSymmetricEJA)
+
+        EXAMPLES::
+
+            sage: J = HadamardEJA(2)
+            sage: J.coordinate_polynomial_ring()
+            Multivariate Polynomial Ring in X1, X2...
+            sage: J = RealSymmetricEJA(3,QQ)
+            sage: J.coordinate_polynomial_ring()
+            Multivariate Polynomial Ring in X1, X2, X3, X4, X5, X6...
+
+        """
+        var_names = tuple( "X%d" % z for z in range(1, self.dimension()+1) )
+        return PolynomialRing(self.base_ring(), var_names)
 
     def inner_product(self, x, y):
         """
@@ -746,6 +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
@@ -854,8 +880,7 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule):
         of" function.
         """
         n = self.dimension()
-        var_names = [ "X" + str(z) for z in range(1,n+1) ]
-        R = PolynomialRing(self.base_ring(), var_names)
+        R = self.coordinate_polynomial_ring()
         vars = R.gens()
         F = R.fraction_field()