X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feuclidean_jordan_algebra.py;h=038de61f481c4036dec9032806f22bdf5d2e2602;hb=eabb7b6ad9c1be19f90c9125e79c00eb09a0b68c;hp=f71f75d690054a0facd849de639d7a0ead3b8cbe;hpb=78eb37d0cec0870b70171688cc8a30a433606e71;p=sage.d.git

diff --git a/mjo/eja/euclidean_jordan_algebra.py b/mjo/eja/euclidean_jordan_algebra.py
index f71f75d..038de61 100644
--- a/mjo/eja/euclidean_jordan_algebra.py
+++ b/mjo/eja/euclidean_jordan_algebra.py
@@ -80,19 +80,6 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
     class Element(FiniteDimensionalAlgebraElement):
         """
         An element of a Euclidean Jordan algebra.
-
-        Since EJAs are commutative, the "right multiplication" matrix is
-        also the left multiplication matrix and must be symmetric::
-
-            sage: set_random_seed()
-            sage: n = ZZ.random_element(1,10).abs()
-            sage: J = eja_rn(5)
-            sage: J.random_element().matrix().is_symmetric()
-            True
-            sage: J = eja_ln(5)
-            sage: J.random_element().matrix().is_symmetric()
-            True
-
         """
 
         def __pow__(self, n):
@@ -111,8 +98,7 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
             EXAMPLES:
 
                 sage: set_random_seed()
-                sage: J = eja_ln(5)
-                sage: x = J.random_element()
+                sage: x = random_eja().random_element()
                 sage: x.matrix()*x.vector() == (x**2).vector()
                 True
 
@@ -181,23 +167,13 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
             The identity element is never nilpotent::
 
                 sage: set_random_seed()
-                sage: n = ZZ.random_element(2,10).abs()
-                sage: J = eja_rn(n)
-                sage: J.one().is_nilpotent()
-                False
-                sage: J = eja_ln(n)
-                sage: J.one().is_nilpotent()
+                sage: random_eja().one().is_nilpotent()
                 False
 
             The additive identity is always nilpotent::
 
                 sage: set_random_seed()
-                sage: n = ZZ.random_element(2,10).abs()
-                sage: J = eja_rn(n)
-                sage: J.zero().is_nilpotent()
-                True
-                sage: J = eja_ln(n)
-                sage: J.zero().is_nilpotent()
+                sage: random_eja().zero().is_nilpotent()
                 True
 
             """
@@ -295,18 +271,14 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
             EXAMPLES::
 
                 sage: set_random_seed()
-                sage: n = ZZ.random_element(1,10).abs()
-                sage: J = eja_rn(n)
-                sage: x = J.random_element()
+                sage: x = random_eja().random_element()
                 sage: x.degree() == x.minimal_polynomial().degree()
                 True
 
             ::
 
                 sage: set_random_seed()
-                sage: n = ZZ.random_element(1,10).abs()
-                sage: J = eja_ln(n)
-                sage: x = J.random_element()
+                sage: x = random_eja().random_element()
                 sage: x.degree() == x.minimal_polynomial().degree()
                 True
 
@@ -371,21 +343,15 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
             TESTS::
 
                 sage: set_random_seed()
-                sage: n = ZZ.random_element(1,10).abs()
-                sage: J = eja_rn(n)
-                sage: x = J.random_element()
-                sage: x.subalgebra_generated_by().is_associative()
-                True
-                sage: J = eja_ln(n)
-                sage: x = J.random_element()
+                sage: x = random_eja().random_element()
                 sage: x.subalgebra_generated_by().is_associative()
                 True
 
             Squaring in the subalgebra should be the same thing as
             squaring in the superalgebra::
 
-                sage: J = eja_ln(5)
-                sage: x = J.random_element()
+                sage: set_random_seed()
+                sage: x = random_eja().random_element()
                 sage: u = x.subalgebra_generated_by().random_element()
                 sage: u.matrix()*u.vector() == (u**2).vector()
                 True
@@ -640,12 +606,24 @@ 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 right-multiplication-by-s matrix by looping
+        # 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.
+        # to find out what the corresponding row should be. BEWARE:
+        # these multiplication tables won't be symmetric! It therefore
+        # becomes REALLY IMPORTANT that the underlying algebra
+        # constructor uses ROW vectors and not COLUMN vectors. That's
+        # why we're computing rows here and not columns.
         Q_rows = []
         for t in S:
             this_row = mat2vec((s*t + t*s)/2)
@@ -654,3 +632,34 @@ 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)