X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;ds=inline;f=mjo%2Feja%2Feja_algebra.py;h=933603a40a7be27feb891efa4b53f3f82388f239;hb=1b6878559ad75aa0064503a962c8c183e13ab91a;hp=c569098b3d3e5d6fbceef6352e22861dd125a7f8;hpb=af79c1d027cf737d125b11fd41bb0bc2150778fb;p=sage.d.git

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index c569098..933603a 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
 
@@ -374,6 +371,28 @@ 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 +765,8 @@ 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 +875,7 @@ 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()