X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_algebra.py;h=af7d059631b1706227e59d54952cfec552ddabb1;hb=47671d4a72c9eaed822c066f05a26f63c7301526;hp=ad6cde724a0d986e92a3c31a2de8ca0baed9563f;hpb=2c0c1339dda541cf9aee33b9becd03e901841499;p=sage.d.git

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index ad6cde7..af7d059 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()
@@ -422,6 +423,18 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
         """
         return "Associative" in self.category().axioms()
 
+    def _is_commutative(self):
+        r"""
+        Whether or not this algebra's multiplication table is commutative.
+
+        This method should of course always return ``True``, unless
+        this algebra was constructed with ``check_axioms=False`` and
+        passed an invalid multiplication table.
+        """
+        return all( self.product_on_basis(i,j) == self.product_on_basis(i,j)
+                    for i in range(self.dimension())
+                    for j in range(self.dimension()) )
+
     def _is_jordanian(self):
         r"""
         Whether or not this algebra's multiplication table respects the
@@ -429,7 +442,7 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
 
         We only check one arrangement of `x` and `y`, so for a
         ``True`` result to be truly true, you should also check
-        :meth:`is_commutative`. This method should of course always
+        :meth:`_is_commutative`. This method should of course always
         return ``True``, unless this algebra was constructed with
         ``check_axioms=False`` and passed an invalid multiplication table.
         """
@@ -455,7 +468,7 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
         if not R.is_exact():
             # This choice is sufficient to allow the construction of
             # QuaternionHermitianEJA(2, field=RDF) with check_axioms=True.
-            epsilon = 1e-16
+            epsilon = 1e-15
 
         for i in range(self.dimension()):
             for j in range(self.dimension()):
@@ -1775,9 +1788,9 @@ 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
 
@@ -2043,9 +2056,9 @@ 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
 
@@ -2340,9 +2353,9 @@ 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