eja: fix complex-unembedding with respect to 5537f4534.

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

diff --git a/mjo/eja/euclidean_jordan_algebra.py b/mjo/eja/euclidean_jordan_algebra.py
index b25839815289ba6f60630a14b790dbfe29f8969b..1e5ada2188c3b6b3834165f221ab20b56d5c1f98 100644 (file)
--- a/mjo/eja/euclidean_jordan_algebra.py
+++ b/mjo/eja/euclidean_jordan_algebra.py
@@ -94,6 +94,20 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
         The inner product associated with this Euclidean Jordan algebra.
 
         Will default to the trace inner product if nothing else.
         The inner product associated with this Euclidean Jordan algebra.
 
         Will default to the trace inner product if nothing else.

+
+        EXAMPLES:
+
+        The inner product must satisfy its axiom for this algebra to truly
+        be a Euclidean Jordan Algebra::
+
+            sage: set_random_seed()
+            sage: J = random_eja()
+            sage: x = J.random_element()
+            sage: y = J.random_element()
+            sage: z = J.random_element()
+            sage: (x*y).inner_product(z) == y.inner_product(x*z)
+            True
+

         """
         if (not x in self) or (not y in self):
             raise TypeError("arguments must live in this algebra")
         """
         if (not x in self) or (not y in self):
             raise TypeError("arguments must live in this algebra")


@@ -1168,13 +1182,13 @@ def _embed_complex_matrix(M):
         sage: x2 = F(1 + 2*i)
         sage: x3 = F(-i)
         sage: x4 = F(6)
         sage: x2 = F(1 + 2*i)
         sage: x3 = F(-i)
         sage: x4 = F(6)

-        sage: M = matrix(F,2,[x1,x2,x3,x4])
+        sage: M = matrix(F,2,[[x1,x2],[x3,x4]])

         sage: _embed_complex_matrix(M)
         sage: _embed_complex_matrix(M)

-        [ 4  2| 1 -2]
-        [-2  4| 2  1]
+        [ 4 -2| 1  2]
+        [ 2  4|-2  1]

         [-----+-----]
         [-----+-----]

-        [ 0  1| 6  0]
-        [-1  0| 0  6]
+        [ 0 -1| 6  0]
+        [ 1  0| 0  6]

 
     """
     n = M.nrows()
 
     """
     n = M.nrows()


@@ -1185,7 +1199,7 @@ def _embed_complex_matrix(M):
     for z in M.list():
         a = z.real()
         b = z.imag()
     for z in M.list():
         a = z.real()
         b = z.imag()

-        blocks.append(matrix(field, 2, [[a,-b],[b,a]]))
+        blocks.append(matrix(field, 2, [[a,b],[-b,a]]))

 
     # We can drop the imaginaries here.
     return block_matrix(field.base_ring(), n, blocks)
 
     # We can drop the imaginaries here.
     return block_matrix(field.base_ring(), n, blocks)


@@ -1202,8 +1216,17 @@ def _unembed_complex_matrix(M):
         ....:                 [ 9,  10, 11, 12],
         ....:                 [-10, 9, -12, 11] ])
         sage: _unembed_complex_matrix(A)
         ....:                 [ 9,  10, 11, 12],
         ....:                 [-10, 9, -12, 11] ])
         sage: _unembed_complex_matrix(A)

-        [  -2*i + 1   -4*i + 3]
-        [ -10*i + 9 -12*i + 11]
+        [  2*i + 1   4*i + 3]
+        [ 10*i + 9 12*i + 11]
+
+    TESTS::
+
+        sage: set_random_seed()
+        sage: F = QuadraticField(-1, 'i')
+        sage: M = random_matrix(F, 3)
+        sage: _unembed_complex_matrix(_embed_complex_matrix(M)) == M
+        True
+

     """
     n = ZZ(M.nrows())
     if M.ncols() != n:
     """
     n = ZZ(M.nrows())
     if M.ncols() != n:


@@ -1224,7 +1247,7 @@ def _unembed_complex_matrix(M):
                 raise ValueError('bad real submatrix')
             if submat[0,1] != -submat[1,0]:
                 raise ValueError('bad imag submatrix')
                 raise ValueError('bad real submatrix')
             if submat[0,1] != -submat[1,0]:
                 raise ValueError('bad imag submatrix')

-            z = submat[0,0] + submat[1,0]*i
+            z = submat[0,0] + submat[0,1]*i

             elements.append(z)
 
     return matrix(F, n/2, elements)
             elements.append(z)
 
     return matrix(F, n/2, elements)