X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_algebra.py;h=d3eac4f6d3bfbad50f6bbc4b371aaa9d39f8859b;hb=d489a9250f943511d4c6349d65bf624e963d49a8;hp=9f8a2585d456b7d82f1c59f1ca067eebf23d0d60;hpb=1d6c0d98ea24be9bcfec236ad94d6d125dabd8f4;p=sage.d.git

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index 9f8a258..d3eac4f 100644
--- 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
@@ -1193,7 +1194,7 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
             sage: x = J.random_element()
             sage: J.one()*x == x and x*J.one() == x
             True
-            sage: A = x.subalgebra_generated_by()
+            sage: A = x.subalgebra_generated_by(orthonormalize=False)
             sage: y = A.random_element()
             sage: A.one()*y == y and y*A.one() == y
             True
@@ -1219,7 +1220,7 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
             sage: actual == expected
             True
             sage: x = J.random_element()
-            sage: A = x.subalgebra_generated_by()
+            sage: A = x.subalgebra_generated_by(orthonormalize=False)
             sage: actual = A.one().operator().matrix()
             sage: expected = matrix.identity(A.base_ring(), A.dimension())
             sage: actual == expected
@@ -1799,14 +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())
@@ -2187,15 +2187,6 @@ class ComplexHermitianEJA(HermitianMatrixEJA, RationalBasisEJA, ConcreteEJA):
         ...
         TypeError: Illegal initializer for algebraic number
 
-    This causes the following error when we try to scale a matrix of
-    complex numbers by an inexact real number::
-
-        sage: ComplexHermitianEJA(2,field=RR)
-        Traceback (most recent call last):
-        ...
-        TypeError: Unable to coerce entries (=(1.00000000000000,
-        -0.000000000000000)) to coefficients in Algebraic Real Field
-
     TESTS:
 
     The dimension of this algebra is `n^2`::