X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_subalgebra.py;h=85ada0705fe8073fa80500d4719c38a5ea16a576;hb=4fcd301b1104a5629e0aa867742f507e882dc25f;hp=024dfbe72ee6fb0f6f7fe2c00648b79a121d13a5;hpb=372770929343f5a75e8e8231894b466b3382dd9d;p=sage.d.git

diff --git a/mjo/eja/eja_subalgebra.py b/mjo/eja/eja_subalgebra.py
index 024dfbe..85ada07 100644
--- a/mjo/eja/eja_subalgebra.py
+++ b/mjo/eja/eja_subalgebra.py
@@ -85,7 +85,28 @@ class FiniteDimensionalEuclideanJordanSubalgebra(FiniteDimensionalEuclideanJorda
     SETUP::
 
         sage: from mjo.eja.eja_algebra import (ComplexHermitianEJA,
-        ....:                                  JordanSpinEJA)
+        ....:                                  JordanSpinEJA,
+        ....:                                  RealSymmetricEJA)
+        sage: from mjo.eja.eja_subalgebra import FiniteDimensionalEuclideanJordanSubalgebra
+
+    EXAMPLES:
+
+    The following Peirce subalgebras of the 2-by-2 real symmetric
+    matrices do not contain the superalgebra's identity element::
+
+        sage: J = RealSymmetricEJA(2)
+        sage: E11 = matrix(AA, [ [1,0],
+        ....:                    [0,0] ])
+        sage: E22 = matrix(AA, [ [0,0],
+        ....:                    [0,1] ])
+        sage: K1 = FiniteDimensionalEuclideanJordanSubalgebra(J, (J(E11),))
+        sage: K1.one().natural_representation()
+        [1 0]
+        [0 0]
+        sage: K2 = FiniteDimensionalEuclideanJordanSubalgebra(J, (J(E22),))
+        sage: K2.one().natural_representation()
+        [0 0]
+        [0 1]
 
     TESTS:
 
@@ -109,7 +130,7 @@ class FiniteDimensionalEuclideanJordanSubalgebra(FiniteDimensionalEuclideanJorda
         1
 
     """
-    def __init__(self, superalgebra, basis, rank=None, category=None):
+    def __init__(self, superalgebra, basis, category=None, check_axioms=True):
         self._superalgebra = superalgebra
         V = self._superalgebra.vector_space()
         field = self._superalgebra.base_ring()
@@ -132,7 +153,11 @@ class FiniteDimensionalEuclideanJordanSubalgebra(FiniteDimensionalEuclideanJorda
         superalgebra_basis = [ self._superalgebra.from_vector(b)
                                for b in basis_vectors ]
 
+        # If our superalgebra is a subalgebra of something else, then
+        # these vectors won't have the right coordinates for
+        # V.span_of_basis() unless we use V.from_vector() on them.
         W = V.span_of_basis( V.from_vector(v) for v in basis_vectors )
+
         n = len(superalgebra_basis)
         mult_table = [[W.zero() for i in range(n)] for j in range(n)]
         for i in range(n):
@@ -154,12 +179,13 @@ class FiniteDimensionalEuclideanJordanSubalgebra(FiniteDimensionalEuclideanJorda
 
 
         fdeja = super(FiniteDimensionalEuclideanJordanSubalgebra, self)
-        return fdeja.__init__(field,
-                              mult_table,
-                              rank,
-                              prefix=prefix,
-                              category=category,
-                              natural_basis=natural_basis)
+        fdeja.__init__(field,
+                       mult_table,
+                       prefix=prefix,
+                       category=category,
+                       natural_basis=natural_basis,
+                       check_field=False,
+                       check_axioms=check_axioms)
 
 
 
@@ -177,7 +203,7 @@ class FiniteDimensionalEuclideanJordanSubalgebra(FiniteDimensionalEuclideanJorda
         EXAMPLES::
 
             sage: J = RealSymmetricEJA(3)
-            sage: X = matrix(QQ, [ [0,0,1],
+            sage: X = matrix(AA, [ [0,0,1],
             ....:                  [0,1,0],
             ....:                  [1,0,0] ])
             sage: x = J(X)
@@ -194,8 +220,12 @@ class FiniteDimensionalEuclideanJordanSubalgebra(FiniteDimensionalEuclideanJorda
         if elt not in self.superalgebra():
             raise ValueError("not an element of this subalgebra")
 
-        coords = self.vector_space().coordinate_vector(elt.to_vector())
-        return self.from_vector(coords)
+        # The extra hackery is because foo.to_vector() might not
+        # live in foo.parent().vector_space()!
+        coords = sum( a*b for (a,b)
+                          in zip(elt.to_vector(),
+                                 self.superalgebra().vector_space().basis()) )
+        return self.from_vector(self.vector_space().coordinate_vector(coords))
 
 
 
@@ -228,10 +258,10 @@ class FiniteDimensionalEuclideanJordanSubalgebra(FiniteDimensionalEuclideanJorda
         EXAMPLES::
 
             sage: J = RealSymmetricEJA(3)
-            sage: E11 = matrix(QQ, [ [1,0,0],
+            sage: E11 = matrix(ZZ, [ [1,0,0],
             ....:                    [0,0,0],
             ....:                    [0,0,0] ])
-            sage: E22 = matrix(QQ, [ [0,0,0],
+            sage: E22 = matrix(ZZ, [ [0,0,0],
             ....:                    [0,1,0],
             ....:                    [0,0,0] ])
             sage: b1 = J(E11)