X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_algebra.py;h=a5653a3e5e4e0fb0297d7a5ebefceff2b7ee75cc;hb=a900f5daa84d0889ce7c1e041fb214a09e8d7bcd;hp=3671e367359d5eeb7b86c76fe98ec4e90edb2f6e;hpb=fa3651ef28df68f4c37b16339074fbf86b8feff4;p=sage.d.git

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index 3671e36..a5653a3 100644
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -34,12 +34,13 @@ for these simple algebras:
   * :class:`QuaternionHermitianEJA`
   * :class:`OctonionHermitianEJA`
 
-In addition to these, we provide two other example constructions,
+In addition to these, we provide a few other example constructions,
 
   * :class:`JordanSpinEJA`
   * :class:`HadamardEJA`
   * :class:`AlbertEJA`
   * :class:`TrivialEJA`
+  * :class:`ComplexSkewSymmetricEJA`
 
 The Jordan spin algebra is a bilinear form algebra where the bilinear
 form is the identity. The Hadamard EJA is simply a Cartesian product
@@ -1447,26 +1448,13 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
         # For a general base ring... maybe we can trust this to do the
         # right thing? Unlikely, but.
         V = self.vector_space()
-        v = V.random_element()
-
-        if self.base_ring() is AA:
-            # The "random element" method of the algebraic reals is
-            # stupid at the moment, and only returns integers between
-            # -2 and 2, inclusive:
-            #
-            #   https://trac.sagemath.org/ticket/30875
-            #
-            # Instead, we implement our own "random vector" method,
-            # and then coerce that into the algebra. We use the vector
-            # space degree here instead of the dimension because a
-            # subalgebra could (for example) be spanned by only two
-            # vectors, each with five coordinates.  We need to
-            # generate all five coordinates.
-            if thorough:
-                v *= QQbar.random_element().real()
-            else:
-                v *= QQ.random_element()
+        if self.base_ring() is AA and not thorough:
+            # Now that AA generates actually random random elements
+            # (post Trac 30875), we only need to de-thorough the
+            # randomness when asked to.
+            V = V.change_ring(QQ)
 
+        v = V.random_element()
         return self.from_vector(V.coordinate_vector(v))
 
     def random_elements(self, count, thorough=False):
@@ -2450,7 +2438,7 @@ class OctonionHermitianEJA(HermitianMatrixEJA, RationalBasisEJA, ConcreteEJA):
     @staticmethod
     def _max_random_instance_size(max_dimension):
         r"""
-        The maximum rank of a random QuaternionHermitianEJA.
+        The maximum rank of a random OctonionHermitianEJA.
         """
         # There's certainly a formula for this, but with only four
         # cases to worry about, I'm not that motivated to derive it.
@@ -3767,3 +3755,9 @@ class ComplexSkewSymmetricEJA(RationalBasisEJA, ConcreteEJA):
                          field=field,
                          matrix_space=A,
                          **kwargs)
+
+        # This algebra is conjectured (by me) to be isomorphic to
+        # the quaternion Hermitian EJA of size n, and the rank
+        # would follow from that.
+        #self.rank.set_cache(n)
+        self.one.set_cache( self(-J) )