eja: change a misleading comment.

[sage.d.git] / mjo / eja / eja_algebra.py

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index afd0f55c103c885315e99bc90afe647262aadfbd..f38128adf646c2dabcdd02cbfc26797731d472a2 100644 (file)
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -1,4 +1,4 @@
-"""
+r"""
 Representations and constructions for Euclidean Jordan algebras.
 
 A Euclidean Jordan algebra is a Jordan algebra that has some
@@ -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):
@@ -1812,14 +1800,13 @@ class RationalBasisEJA(FiniteDimensionalEJA):
             # Bypass the hijinks if they won't benefit us.
             return super()._charpoly_coefficients()
 
-        # Do the computation over the rationals. The answer will be
-        # the same, because all we've done is a change of basis.
-        # Then, change back from QQ to our real base ring
+        # Do the computation over the rationals.
         a = ( a_i.change_ring(self.base_ring())
               for a_i in self.rational_algebra()._charpoly_coefficients() )
 
-        # Otherwise, convert the coordinate variables back to the
-        # deorthonormalized ones.
+        # Convert our coordinate variables into deorthonormalized ones
+        # and substitute them into the deorthonormalized charpoly
+        # coefficients.
         R = self.coordinate_polynomial_ring()
         from sage.modules.free_module_element import vector
         X = vector(R, R.gens())