X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feuclidean_jordan_algebra.py;h=624806fddac93c9292b229d6afd7954224827e87;hb=7c384faefd026dd4010e30399646e2e4cb5b4b27;hp=be281bfb99d0ef86e73fa7d4a2d3643f54d605e3;hpb=83f719b66100fdb5bf5035355c48b5337be6b11e;p=sage.d.git

diff --git a/mjo/eja/euclidean_jordan_algebra.py b/mjo/eja/euclidean_jordan_algebra.py
index be281bf..624806f 100644
--- a/mjo/eja/euclidean_jordan_algebra.py
+++ b/mjo/eja/euclidean_jordan_algebra.py
@@ -5,13 +5,30 @@ are used in optimization, and have some additional nice methods beyond
 what can be supported in a general Jordan Algebra.
 """
 
-from sage.all import *
+from sage.structure.unique_representation import UniqueRepresentation
+from sage.algebras.finite_dimensional_algebras.finite_dimensional_algebra import FiniteDimensionalAlgebra
+
+class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
+    @staticmethod
+    def __classcall__(cls, field, mult_table, names='e', category=None):
+        fda = super(FiniteDimensionalEuclideanJordanAlgebra, cls)
+        return fda.__classcall_private__(cls,
+                                         field,
+                                         mult_table,
+                                         names,
+                                         category)
+
+    def __init__(self, field, mult_table, names='e', category=None):
+        fda = super(FiniteDimensionalEuclideanJordanAlgebra, self)
+        fda.__init__(field, mult_table, names, category)
+
+
+    def _repr_(self):
+        """
+        Return a string representation of ``self``.
+        """
+        return "Euclidean Jordan algebra of degree {} over {}".format(self.degree(), self.base_ring())
 
-def eja_minimal_polynomial(x):
-    """
-    Return the minimal polynomial of ``x`` in its parent EJA
-    """
-    return x._x.matrix().minimal_polynomial()
 
 
 def eja_rn(dimension, field=QQ):
@@ -46,13 +63,16 @@ def eja_rn(dimension, field=QQ):
     # component of x; and likewise for the ith basis element e_i.
     Qs = [ matrix(field, dimension, dimension, lambda k,j: 1*(k == j == i))
            for i in xrange(dimension) ]
-    A = FiniteDimensionalAlgebra(QQ,Qs,assume_associative=True)
-    return JordanAlgebra(A)
+
+    # Assuming associativity is wrong here, but it works to
+    # temporarily trick the Jordan algebra constructor into using the
+    # multiplication table.
+    return FiniteDimensionalEuclideanJordanAlgebra(field,Qs)
 
 
 def eja_ln(dimension, field=QQ):
     """
-    Return the Jordan algebra corresponding to the Lorenzt "ice cream"
+    Return the Jordan algebra corresponding to the Lorentz "ice cream"
     cone of the given ``dimension``.
 
     EXAMPLES:
@@ -97,5 +117,4 @@ def eja_ln(dimension, field=QQ):
         Qi[0,0] = Qi[0,0] * ~field(2)
         Qs.append(Qi)
 
-    A = FiniteDimensionalAlgebra(QQ,Qs,assume_associative=True)
-    return JordanAlgebra(A)
+    return FiniteDimensionalEuclideanJordanAlgebra(field,Qs)