X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_algebra.py;h=3390df7545bb41257ee58c68f04154ce7a18d462;hb=88eb54dba783144477d35d2b246bff15df438c2e;hp=ccc5006f3d79397d81ad98bbf45a7262e36dd6e9;hpb=d227f7ece4e6eb41af3ad0671cd0a2a6ee33b5c1;p=sage.d.git

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index ccc5006..3390df7 100644
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -311,9 +311,9 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
         return ``True``, unless this algebra was constructed with
         ``check_axioms=False`` and passed an invalid multiplication table.
         """
-        return all( (self.monomial(i)**2)*(self.monomial(i)*self.monomial(j))
+        return all( (self.gens()[i]**2)*(self.gens()[i]*self.gens()[j])
                     ==
-                    (self.monomial(i))*((self.monomial(i)**2)*self.monomial(j))
+                    (self.gens()[i])*((self.gens()[i]**2)*self.gens()[j])
                     for i in range(self.dimension())
                     for j in range(self.dimension()) )
 
@@ -335,9 +335,9 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
         for i in range(self.dimension()):
             for j in range(self.dimension()):
                 for k in range(self.dimension()):
-                    x = self.monomial(i)
-                    y = self.monomial(j)
-                    z = self.monomial(k)
+                    x = self.gens()[i]
+                    y = self.gens()[j]
+                    z = self.gens()[k]
                     diff = (x*y).inner_product(z) - x.inner_product(y*z)
 
                     if self.base_ring().is_exact():
@@ -660,8 +660,8 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
 
         # And to each subsequent row, prepend an entry that belongs to
         # the left-side "header column."
-        M += [ [self.monomial(i)] + [ self.product_on_basis(i,j)
-                                      for j in range(n) ]
+        M += [ [self.gens()[i]] + [ self.product_on_basis(i,j)
+                                    for j in range(n) ]
                for i in range(n) ]
 
         return table(M, header_row=True, header_column=True, frame=True)
@@ -1129,7 +1129,7 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
         def L_x_i_j(i,j):
             # From a result in my book, these are the entries of the
             # basis representation of L_x.
-            return sum( vars[k]*self.monomial(k).operator().matrix()[i,j]
+            return sum( vars[k]*self.gens()[k].operator().matrix()[i,j]
                         for k in range(n) )
 
         L_x = matrix(F, n, n, L_x_i_j)
@@ -2730,6 +2730,33 @@ class CartesianProductEJA(CombinatorialFreeModule_CartesianProduct,
         Real Field (+) Euclidean Jordan algebra of dimension 6 over
         Algebraic Real Field
 
+    Rank is additive on a Cartesian product::
+
+        sage: J1 = HadamardEJA(1)
+        sage: J2 = RealSymmetricEJA(2)
+        sage: J = cartesian_product([J1,J2])
+        sage: J1.rank.clear_cache()
+        sage: J2.rank.clear_cache()
+        sage: J.rank.clear_cache()
+        sage: J.rank()
+        3
+        sage: J.rank() == J1.rank() + J2.rank()
+        True
+
+    The same rank computation works over the rationals, with whatever
+    basis you like::
+
+        sage: J1 = HadamardEJA(1, field=QQ, orthonormalize=False)
+        sage: J2 = RealSymmetricEJA(2, field=QQ, orthonormalize=False)
+        sage: J = cartesian_product([J1,J2])
+        sage: J1.rank.clear_cache()
+        sage: J2.rank.clear_cache()
+        sage: J.rank.clear_cache()
+        sage: J.rank()
+        3
+        sage: J.rank() == J1.rank() + J2.rank()
+        True
+
     TESTS:
 
     All factors must share the same base field::
@@ -2753,7 +2780,6 @@ class CartesianProductEJA(CombinatorialFreeModule_CartesianProduct,
         True
         sage: x.inner_product(y) == J.cartesian_inner_product(x,y)
         True
-
     """
     def __init__(self, modules, **kwargs):
         CombinatorialFreeModule_CartesianProduct.__init__(self,