eja: fix screwup introduced in 5d147bd962.

[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 16ce256f244e96d7875bda4e3a27d005ae4b3c40..d6b183f8fbfc75799ed63bc5e7ae21d2a85e8b6a 100644 (file)
--- a/mjo/eja/euclidean_jordan_algebra.py
+++ b/mjo/eja/euclidean_jordan_algebra.py
@@ -709,7 +709,7 @@ def _multiplication_table_from_matrix_basis(basis):
     S = [ vec2mat(b) for b in W.basis() ]
 
     Qs = []
-    for s in basis:
+    for s in S:
         # Brute force the multiplication-by-s matrix by looping
         # through all elements of the basis and doing the computation
         # to find out what the corresponding row should be. BEWARE:
@@ -718,7 +718,7 @@ def _multiplication_table_from_matrix_basis(basis):
         # constructor uses ROW vectors and not COLUMN vectors. That's
         # why we're computing rows here and not columns.
         Q_rows = []
-        for t in basis:
+        for t in S:
             this_row = mat2vec((s*t + t*s)/2)
             Q_rows.append(W.coordinates(this_row))
         Q = matrix(field,Q_rows)
@@ -727,6 +727,40 @@ def _multiplication_table_from_matrix_basis(basis):
     return Qs
 
 
+def _embed_complex_matrix(M):
+    """
+    Embed the n-by-n complex matrix ``M`` into the space of real
+    matrices of size 2n-by-2n via the map the sends each entry `z = a +
+    bi` to the block matrix ``[[a,b],[-b,a]]``.
+
+    EXAMPLES::
+
+        sage: F = QuadraticField(-1,'i')
+        sage: x1 = F(4 - 2*i)
+        sage: x2 = F(1 + 2*i)
+        sage: x3 = F(-i)
+        sage: x4 = F(6)
+        sage: M = matrix(F,2,[x1,x2,x3,x4])
+        sage: _embed_complex_matrix(M)
+        [ 4  2| 1 -2]
+        [-2  4| 2  1]
+        [-----+-----]
+        [ 0  1| 6  0]
+        [-1  0| 0  6]
+
+    """
+    n = M.nrows()
+    if M.ncols() != n:
+        raise ArgumentError("the matrix 'M' must be square")
+    field = M.base_ring()
+    blocks = []
+    for z in M.list():
+        a = z.real()
+        b = z.imag()
+        blocks.append(matrix(field, 2, [[a,-b],[b,a]]))
+    return block_matrix(field, n, blocks)
+
+
 def RealSymmetricSimpleEJA(n):
     """
     The rank-n simple EJA consisting of real symmetric n-by-n