X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_algebra.py;h=e79b0e8048debc968629fbd2ad5ada522829b3d6;hb=d6b4042f69335c3f1ad86c0918d28a3d15775e07;hp=c6a82caa9cf74ba78d44fe0db88668805d973e44;hpb=a811b47129cc0e39d3cb4b5f24504426adff3a88;p=sage.d.git

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index c6a82ca..e79b0e8 100644
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -178,7 +178,8 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
 
 
         category = MagmaticAlgebras(field).FiniteDimensional()
-        category = category.WithBasis().Unital()
+        category = category.WithBasis().Unital().Commutative()
+
         if associative:
             # Element subalgebras can take advantage of this.
             category = category.Associative()
@@ -448,11 +449,14 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
         this algebra was constructed with ``check_axioms=False`` and
         passed an invalid Jordan or inner-product.
         """
+        R = self.base_ring()
 
-        # Used to check whether or not something is zero in an inexact
-        # ring. This number is sufficient to allow the construction of
-        # QuaternionHermitianEJA(2, field=RDF) with check_axioms=True.
-        epsilon = 1e-16
+        # Used to check whether or not something is zero.
+        epsilon = R.zero()
+        if not R.is_exact():
+            # This choice is sufficient to allow the construction of
+            # QuaternionHermitianEJA(2, field=RDF) with check_axioms=True.
+            epsilon = 1e-15
 
         for i in range(self.dimension()):
             for j in range(self.dimension()):
@@ -462,12 +466,8 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
                     z = self.gens()[k]
                     diff = (x*y).inner_product(z) - x.inner_product(y*z)
 
-                    if self.base_ring().is_exact():
-                        if diff != 0:
-                            return False
-                    else:
-                        if diff.abs() > epsilon:
-                            return False
+                    if diff.abs() > epsilon:
+                        return False
 
         return True
 
@@ -1776,9 +1776,9 @@ class RealSymmetricEJA(ConcreteEJA, RealMatrixEJA):
 
     In theory, our "field" can be any subfield of the reals::
 
-        sage: RealSymmetricEJA(2, field=RDF)
+        sage: RealSymmetricEJA(2, field=RDF, check_axioms=True)
         Euclidean Jordan algebra of dimension 3 over Real Double Field
-        sage: RealSymmetricEJA(2, field=RR)
+        sage: RealSymmetricEJA(2, field=RR, check_axioms=True)
         Euclidean Jordan algebra of dimension 3 over Real Field with
         53 bits of precision
 
@@ -2044,9 +2044,9 @@ class ComplexHermitianEJA(ConcreteEJA, ComplexMatrixEJA):
 
     In theory, our "field" can be any subfield of the reals::
 
-        sage: ComplexHermitianEJA(2, field=RDF)
+        sage: ComplexHermitianEJA(2, field=RDF, check_axioms=True)
         Euclidean Jordan algebra of dimension 4 over Real Double Field
-        sage: ComplexHermitianEJA(2, field=RR)
+        sage: ComplexHermitianEJA(2, field=RR, check_axioms=True)
         Euclidean Jordan algebra of dimension 4 over Real Field with
         53 bits of precision
 
@@ -2341,9 +2341,9 @@ class QuaternionHermitianEJA(ConcreteEJA, QuaternionMatrixEJA):
 
     In theory, our "field" can be any subfield of the reals::
 
-        sage: QuaternionHermitianEJA(2, field=RDF)
+        sage: QuaternionHermitianEJA(2, field=RDF, check_axioms=True)
         Euclidean Jordan algebra of dimension 6 over Real Double Field
-        sage: QuaternionHermitianEJA(2, field=RR)
+        sage: QuaternionHermitianEJA(2, field=RR, check_axioms=True)
         Euclidean Jordan algebra of dimension 6 over Real Field with
         53 bits of precision