X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_subalgebra.py;h=68f1ce4cf8b5f07087e4474069ad4ebe5c6a4998;hb=3f49e3bf2b85b1918c1abb0e8973a6f203dabc86;hp=92fd296b3003a06e7bafb79f9d9c37d9cb6b13cb;hpb=d395668ab9c439d2ee5ec6224d2061656da5ae04;p=sage.d.git

diff --git a/mjo/eja/eja_subalgebra.py b/mjo/eja/eja_subalgebra.py
index 92fd296..68f1ce4 100644
--- a/mjo/eja/eja_subalgebra.py
+++ b/mjo/eja/eja_subalgebra.py
@@ -1,4 +1,5 @@
 from sage.matrix.constructor import matrix
+from sage.misc.cachefunc import cached_method
 
 from mjo.eja.eja_algebra import FiniteDimensionalEJA
 from mjo.eja.eja_element import FiniteDimensionalEJAElement
@@ -51,20 +52,20 @@ class FiniteDimensionalEJASubalgebraElement(FiniteDimensionalEJAElement):
             sage: J = RealSymmetricEJA(3)
             sage: x = sum(J.gens())
             sage: x
-            e0 + e1 + e2 + e3 + e4 + e5
+            b0 + b1 + b2 + b3 + b4 + b5
             sage: A = x.subalgebra_generated_by(orthonormalize=False)
             sage: A(x)
-            f1
+            c1
             sage: A(x).superalgebra_element()
-            e0 + e1 + e2 + e3 + e4 + e5
+            b0 + b1 + b2 + b3 + b4 + b5
             sage: y = sum(A.gens())
             sage: y
-            f0 + f1
+            c0 + c1
             sage: B = y.subalgebra_generated_by(orthonormalize=False)
             sage: B(y)
-            g1
+            d1
             sage: B(y).superalgebra_element()
-            f0 + f1
+            c0 + c1
 
         TESTS:
 
@@ -84,7 +85,7 @@ class FiniteDimensionalEJASubalgebraElement(FiniteDimensionalEJAElement):
             True
 
         """
-        return self.parent().superalgebra()(self.to_matrix())
+        return self.parent().superalgebra_embedding()(self)
 
 
 
@@ -121,17 +122,18 @@ class FiniteDimensionalEJASubalgebra(FiniteDimensionalEJA):
 
     TESTS:
 
-    Ensure that our generator names don't conflict with the superalgebra::
+    Ensure that our generator names don't conflict with the
+    superalgebra::
 
         sage: J = JordanSpinEJA(3)
         sage: J.one().subalgebra_generated_by().gens()
-        (f0,)
+        (c0,)
         sage: J = JordanSpinEJA(3, prefix='f')
         sage: J.one().subalgebra_generated_by().gens()
         (g0,)
-        sage: J = JordanSpinEJA(3, prefix='b')
+        sage: J = JordanSpinEJA(3, prefix='a')
         sage: J.one().subalgebra_generated_by().gens()
-        (c0,)
+        (b0,)
 
     Ensure that we can find subalgebras of subalgebras::
 
@@ -139,7 +141,6 @@ class FiniteDimensionalEJASubalgebra(FiniteDimensionalEJA):
         sage: B = A.one().subalgebra_generated_by()
         sage: B.dimension()
         1
-
     """
     def __init__(self, superalgebra, basis, **kwargs):
         self._superalgebra = superalgebra
@@ -152,7 +153,7 @@ class FiniteDimensionalEJASubalgebra(FiniteDimensionalEJA):
         # try to "increment" the parent algebra's prefix, although
         # this idea goes out the window fast because some prefixen
         # are off-limits.
-        prefixen = [ 'f', 'g', 'h', 'a', 'b', 'c', 'd' ]
+        prefixen = ["b","c","d","e","f","g","h","l","m"]
         try:
             prefix = prefixen[prefixen.index(self._superalgebra.prefix()) + 1]
         except ValueError:
@@ -171,6 +172,7 @@ class FiniteDimensionalEJASubalgebra(FiniteDimensionalEJA):
                          jordan_product,
                          inner_product,
                          field=field,
+                         matrix_space=superalgebra.matrix_space(),
                          prefix=prefix,
                          **kwargs)
 
@@ -200,9 +202,9 @@ class FiniteDimensionalEJASubalgebra(FiniteDimensionalEJA):
             ....:                                    associative=True,
             ....:                                    orthonormalize=False)
             sage: K(J.one())
-            f1
+            c1
             sage: K(J.one() + x)
-            f0 + f1
+            c0 + c1
 
         ::
 
@@ -213,19 +215,6 @@ class FiniteDimensionalEJASubalgebra(FiniteDimensionalEJA):
             return super()._element_constructor_(elt)
 
 
-
-    def matrix_space(self):
-        """
-        Return the matrix space of this algebra, which is identical to
-        that of its superalgebra.
-
-        This is correct "by definition," and avoids a mismatch when
-        the subalgebra is trivial (with no matrix basis elements to
-        infer anything from) and the parent is not.
-        """
-        return self.superalgebra().matrix_space()
-
-
     def superalgebra(self):
         """
         Return the superalgebra that this algebra was generated from.
@@ -233,4 +222,35 @@ class FiniteDimensionalEJASubalgebra(FiniteDimensionalEJA):
         return self._superalgebra
 
 
+    @cached_method
+    def superalgebra_embedding(self):
+        r"""
+        Return the embedding from this subalgebra into the superalgebra.
+
+        EXAMPLES::
+
+            sage: J = HadamardEJA(4)
+            sage: A = J.one().subalgebra_generated_by()
+            sage: iota = A.superalgebra_embedding()
+            sage: iota
+            Linear operator between finite-dimensional Euclidean Jordan algebras represented by the matrix:
+            [1/2]
+            [1/2]
+            [1/2]
+            [1/2]
+            Domain: Euclidean Jordan algebra of dimension 1 over Algebraic Real Field
+            Codomain: Euclidean Jordan algebra of dimension 4 over Algebraic Real Field
+            sage: iota(A.one()) == J.one()
+            True
+
+        """
+        from mjo.eja.eja_operator import FiniteDimensionalEJAOperator
+        mm = self._module_morphism(lambda j: self.superalgebra()(self.monomial(j).to_matrix()),
+                                   codomain=self.superalgebra())
+        return FiniteDimensionalEJAOperator(self,
+                                            self.superalgebra(),
+                                            mm.matrix())
+
+
+
     Element = FiniteDimensionalEJASubalgebraElement