eja: fix recently broken doctests.

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index 5dee5d012d6c19d6fc5d79f804ad8aff2757c3d0..52e27de8c0bb1a9bc69bdb433bd9641b07b2bb90 100644 (file)
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -1523,15 +1523,29 @@ class MatrixEuclideanJordanAlgebra:
         This gives the same answer as it would if we computed the trace
         from the unembedded (original) matrices::
 
+            sage: set_random_seed()
+            sage: J = RealSymmetricEJA.random_instance()
+            sage: x,y = J.random_elements(2)
+            sage: Xe = x.to_matrix()
+            sage: Ye = y.to_matrix()
+            sage: X = J.real_unembed(Xe)
+            sage: Y = J.real_unembed(Ye)
+            sage: expected = (X*Y).trace()
+            sage: actual = J.trace_inner_product(Xe,Ye)
+            sage: actual == expected
+            True
+
+        ::
+
             sage: set_random_seed()
             sage: J = ComplexHermitianEJA.random_instance()
             sage: x,y = J.random_elements(2)
             sage: Xe = x.to_matrix()
             sage: Ye = y.to_matrix()
-            sage: X = ComplexHermitianEJA.real_unembed(Xe)
-            sage: Y = ComplexHermitianEJA.real_unembed(Ye)
+            sage: X = J.real_unembed(Xe)
+            sage: Y = J.real_unembed(Ye)
             sage: expected = (X*Y).trace().real()
-            sage: actual = ComplexHermitianEJA.trace_inner_product(Xe,Ye)
+            sage: actual = J.trace_inner_product(Xe,Ye)
             sage: actual == expected
             True
 
@@ -1542,10 +1556,10 @@ class MatrixEuclideanJordanAlgebra:
             sage: x,y = J.random_elements(2)
             sage: Xe = x.to_matrix()
             sage: Ye = y.to_matrix()
-            sage: X = QuaternionHermitianEJA.real_unembed(Xe)
-            sage: Y = QuaternionHermitianEJA.real_unembed(Ye)
+            sage: X = J.real_unembed(Xe)
+            sage: Y = J.real_unembed(Ye)
             sage: expected = (X*Y).trace().coefficient_tuple()[0]
-            sage: actual = QuaternionHermitianEJA.trace_inner_product(Xe,Ye)
+            sage: actual = J.trace_inner_product(Xe,Ye)
             sage: actual == expected
             True
 
@@ -1556,12 +1570,12 @@ class MatrixEuclideanJordanAlgebra:
 
         try:
             # Works in QQ, AA, RDF, et cetera.
-            return tr.real() / cls.dimension_over_reals()
+            return tr.real()
         except AttributeError:
             # A quaternion doesn't have a real() method, but does
             # have coefficient_tuple() method that returns the
             # coefficients of 1, i, j, and k -- in that order.
-            return tr.coefficient_tuple()[0] / cls.dimension_over_reals()
+            return tr.coefficient_tuple()[0]
 
 
 class RealMatrixEuclideanJordanAlgebra(MatrixEuclideanJordanAlgebra):
@@ -1803,11 +1817,19 @@ class ComplexMatrixEuclideanJordanAlgebra(MatrixEuclideanJordanAlgebra):
         field = M.base_ring()
         R = PolynomialRing(field, 'z')
         z = R.gen()
+
+        # Sage doesn't know how to adjoin the complex "i" (the root of
+        # x^2 + 1) to a field in a general way. Here, we just enumerate
+        # all of the cases that I have cared to support so far.
         if field is AA:
             # Sage doesn't know how to embed AA into QQbar, i.e. how
             # to adjoin sqrt(-1) to AA.
             F = QQbar
+        elif not field.is_exact():
+            # RDF or RR
+            F = field.complex_field()
         else:
+            # Works for QQ and... maybe some other fields.
             F = field.extension(z**2 + 1, 'I', embedding=CLF(-1).sqrt())
         i = F.gen()