eja: remove an unused import.

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

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index 799490044dbb4d0834577f435afd2dbc89429baf..da008d0cf70249de27ac1a52b1d53ae4be9ef4f2 100644 (file)
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -64,8 +64,7 @@ from itertools import repeat
 from sage.algebras.quatalg.quaternion_algebra import QuaternionAlgebra
 from sage.categories.magmatic_algebras import MagmaticAlgebras
 from sage.categories.sets_cat import cartesian_product
-from sage.combinat.free_module import (CombinatorialFreeModule,
-                                       CombinatorialFreeModule_CartesianProduct)
+from sage.combinat.free_module import CombinatorialFreeModule
 from sage.matrix.constructor import matrix
 from sage.matrix.matrix_space import MatrixSpace
 from sage.misc.cachefunc import cached_method
@@ -1837,18 +1836,13 @@ class MatrixEJA:
             True
 
         """
-        Xu = cls.real_unembed(X)
-        Yu = cls.real_unembed(Y)
-        tr = (Xu*Yu).trace()
-
-        try:
-            # Works in QQ, AA, RDF, et cetera.
-            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]
+        # This does in fact compute the real part of the trace.
+        # If we compute the trace of e.g. a complex matrix M,
+        # then we do so by adding up its diagonal entries --
+        # call them z_1 through z_n. The real embedding of z_1
+        # will be a 2-by-2 REAL matrix [a, b; -b, a] whose trace
+        # as a REAL matrix will be 2*a = 2*Re(z_1). And so forth.
+        return (X*Y).trace()/cls.dimension_over_reals()
 
 
 class RealMatrixEJA(MatrixEJA):
@@ -3480,17 +3474,15 @@ class RationalBasisCartesianProductEJA(CartesianProductEJA,
 
 RationalBasisEJA.CartesianProduct = RationalBasisCartesianProductEJA
 
-random_eja = ConcreteEJA.random_instance
-
-# def random_eja(*args, **kwargs):
-#     J1 = ConcreteEJA.random_instance(*args, **kwargs)
-
-#     # This might make Cartesian products appear roughly as often as
-#     # any other ConcreteEJA.
-#     if ZZ.random_element(len(ConcreteEJA.__subclasses__()) + 1) == 0:
-#         # Use random_eja() again so we can get more than two factors.
-#         J2 = random_eja(*args, **kwargs)
-#         J = cartesian_product([J1,J2])
-#         return J
-#     else:
-#         return J1
+def random_eja(*args, **kwargs):
+    J1 = ConcreteEJA.random_instance(*args, **kwargs)
+
+    # This might make Cartesian products appear roughly as often as
+    # any other ConcreteEJA.
+    if ZZ.random_element(len(ConcreteEJA.__subclasses__()) + 1) == 0:
+        # Use random_eja() again so we can get more than two factors.
+        J2 = random_eja(*args, **kwargs)
+        J = cartesian_product([J1,J2])
+        return J
+    else:
+        return J1