eja: fix the basis order for Sn.

[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 c47f4003690905278904327e63ddaf7dcf9e0b44..802171fb0c4cc029c43d4fb4b17004d76bb938ed 100644 (file)
--- a/mjo/eja/euclidean_jordan_algebra.py
+++ b/mjo/eja/euclidean_jordan_algebra.py
@@ -384,6 +384,7 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
             Squaring in the subalgebra should be the same thing as
             squaring in the superalgebra::
 
+                sage: set_random_seed()
                 sage: J = eja_ln(5)
                 sage: x = J.random_element()
                 sage: u = x.subalgebra_generated_by().random_element()
@@ -640,8 +641,16 @@ def eja_sn(dimension, field=QQ):
     def mat2vec(m):
         return vector(field, m.list())
 
+    def vec2mat(v):
+        return matrix(field, dimension, v.list())
+
     W = V.span( mat2vec(s) for s in S )
 
+    # Taking the span above reorders our basis (thanks, jerk!) so we
+    # need to put our "matrix basis" in the same order as the
+    # (reordered) vector basis.
+    S = [ vec2mat(b) for b in W.basis() ]
+
     for s in S:
         # Brute force the multiplication-by-s matrix by looping
         # through all elements of the basis and doing the computation
@@ -658,3 +667,34 @@ def eja_sn(dimension, field=QQ):
         Qs.append(Q)
 
     return FiniteDimensionalEuclideanJordanAlgebra(field,Qs,rank=dimension)
+
+
+def random_eja():
+    """
+    Return a "random" finite-dimensional Euclidean Jordan Algebra.
+
+    ALGORITHM:
+
+    For now, we choose a random natural number ``n`` (greater than zero)
+    and then give you back one of the following:
+
+      * The cartesian product of the rational numbers ``n`` times; this is
+        ``QQ^n`` with the Hadamard product.
+
+      * The Jordan spin algebra on ``QQ^n``.
+
+      * The ``n``-by-``n`` rational symmetric matrices with the symmetric
+        product.
+
+    Later this might be extended to return Cartesian products of the
+    EJAs above.
+
+    TESTS::
+
+        sage: random_eja()
+        Euclidean Jordan algebra of degree...
+
+    """
+    n = ZZ.random_element(1,10).abs()
+    constructor = choice([eja_rn, eja_ln, eja_sn])
+    return constructor(dimension=n, field=QQ)