eja: simplify two random statements.

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

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index 83ec50e5a215417811fe09d72c61251081772160..5deb5c9488431b56678b7b2346eba5681955f92d 100644 (file)
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -1721,9 +1721,10 @@ class ComplexMatrixEJA(MatrixEJA):
 
         blocks = []
         for z in M.list():
-            a = z.list()[0] # real part, I guess
-            b = z.list()[1] # imag part, I guess
-            blocks.append(matrix(field, 2, [[a,b],[-b,a]]))
+            a = z.real()
+            b = z.imag()
+            blocks.append(matrix(field, 2, [ [ a, b],
+                                             [-b, a] ]))
 
         return matrix.block(field, n, blocks)
 
@@ -1877,7 +1878,6 @@ class ComplexHermitianEJA(ConcreteEJA, ComplexMatrixEJA):
 
             sage: set_random_seed()
             sage: n = ZZ.random_element(1,5)
-            sage: field = QuadraticField(2, 'sqrt2')
             sage: B = ComplexHermitianEJA._denormalized_basis(n)
             sage: all( M.is_symmetric() for M in  B)
             True
@@ -1895,18 +1895,27 @@ class ComplexHermitianEJA(ConcreteEJA, ComplexMatrixEJA):
         #   * The diagonal will (as a result) be real.
         #
         S = []
+        Eij = matrix.zero(F,n)
         for i in range(n):
             for j in range(i+1):
-                Eij = matrix(F, n, lambda k,l: k==i and l==j)
+                # "build" E_ij
+                Eij[i,j] = 1
                 if i == j:
                     Sij = cls.real_embed(Eij)
                     S.append(Sij)
                 else:
                     # The second one has a minus because it's conjugated.
-                    Sij_real = cls.real_embed(Eij + Eij.transpose())
+                    Eij[j,i] = 1 # Eij = Eij + Eij.transpose()
+                    Sij_real = cls.real_embed(Eij)
                     S.append(Sij_real)
-                    Sij_imag = cls.real_embed(I*Eij - I*Eij.transpose())
+                    # Eij = I*Eij - I*Eij.transpose()
+                    Eij[i,j] = I
+                    Eij[j,i] = -I
+                    Sij_imag = cls.real_embed(Eij)
                     S.append(Sij_imag)
+                    Eij[j,i] = 0
+                # "erase" E_ij
+                Eij[i,j] = 0
 
         # Since we embedded these, we can drop back to the "field" that we
         # started with instead of the complex extension "F".
@@ -2162,23 +2171,39 @@ class QuaternionHermitianEJA(ConcreteEJA, QuaternionMatrixEJA):
         #   * The diagonal will (as a result) be real.
         #
         S = []
+        Eij = matrix.zero(Q,n)
         for i in range(n):
             for j in range(i+1):
-                Eij = matrix(Q, n, lambda k,l: k==i and l==j)
+                # "build" E_ij
+                Eij[i,j] = 1
                 if i == j:
                     Sij = cls.real_embed(Eij)
                     S.append(Sij)
                 else:
                     # The second, third, and fourth ones have a minus
                     # because they're conjugated.
-                    Sij_real = cls.real_embed(Eij + Eij.transpose())
+                    # Eij = Eij + Eij.transpose()
+                    Eij[j,i] = 1
+                    Sij_real = cls.real_embed(Eij)
                     S.append(Sij_real)
-                    Sij_I = cls.real_embed(I*Eij - I*Eij.transpose())
+                    # Eij = I*(Eij - Eij.transpose())
+                    Eij[i,j] = I
+                    Eij[j,i] = -I
+                    Sij_I = cls.real_embed(Eij)
                     S.append(Sij_I)
-                    Sij_J = cls.real_embed(J*Eij - J*Eij.transpose())
+                    # Eij = J*(Eij - Eij.transpose())
+                    Eij[i,j] = J
+                    Eij[j,i] = -J
+                    Sij_J = cls.real_embed(Eij)
                     S.append(Sij_J)
-                    Sij_K = cls.real_embed(K*Eij - K*Eij.transpose())
+                    # Eij = K*(Eij - Eij.transpose())
+                    Eij[i,j] = K
+                    Eij[j,i] = -K
+                    Sij_K = cls.real_embed(Eij)
                     S.append(Sij_K)
+                    Eij[j,i] = 0
+                # "erase" E_ij
+                Eij[i,j] = 0
 
         # Since we embedded these, we can drop back to the "field" that we
         # started with instead of the quaternion algebra "Q".