eja: implement subalgebra_generated_by() in terms of the new class.

[sage.d.git] / mjo / eja / eja_subalgebra.py

diff --git a/mjo/eja/eja_subalgebra.py b/mjo/eja/eja_subalgebra.py
index 7c883d92fab3f3f2ee158737bdb0ec12bdf7effd..0ff3519fa15ba4eb1e968ca64d92e69326368b1e 100644 (file)
--- a/mjo/eja/eja_subalgebra.py
+++ b/mjo/eja/eja_subalgebra.py
@@ -16,7 +16,7 @@ class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclide
         # First compute the vector subspace spanned by the powers of
         # the given element.
         V = superalgebra.vector_space()
-        eja_basis = [superalgebra.one()]
+        superalgebra_basis = [superalgebra.one()]
         basis_vectors = [superalgebra.one().vector()]
         W = V.span_of_basis(basis_vectors)
         for exponent in range(1, V.dimension()):
@@ -24,21 +24,21 @@ class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclide
             basis_vectors.append( new_power.vector() )
             try:
                 W = V.span_of_basis(basis_vectors)
-                eja_basis.append( new_power )
+                superalgebra_basis.append( new_power )
             except ValueError:
                 # Vectors weren't independent; bail and keep the
                 # last subspace that worked.
                 break
 
         # Make the basis hashable for UniqueRepresentation.
-        eja_basis = tuple(eja_basis)
+        superalgebra_basis = tuple(superalgebra_basis)
 
         # Now figure out the entries of the right-multiplication
         # matrix for the successive basis elements b0, b1,... of
         # that subspace.
         F = superalgebra.base_ring()
         mult_table = []
-        for b_right in eja_basis:
+        for b_right in superalgebra_basis:
                 b_right_rows = []
                 # The first row of the right-multiplication matrix by
                 # b1 is what we get if we apply that matrix to b1. The
@@ -47,7 +47,7 @@ class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclide
                 #
                 # IMPORTANT: this assumes that all vectors are COLUMN
                 # vectors, unlike our superclass (which uses row vectors).
-                for b_left in eja_basis:
+                for b_left in superalgebra_basis:
                     # Multiply in the original EJA, but then get the
                     # coordinates from the subalgebra in terms of its
                     # basis.
@@ -87,7 +87,7 @@ class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclide
                                    F,
                                    mult_table,
                                    rank,
-                                   eja_basis,
+                                   superalgebra_basis,
                                    W,
                                    assume_associative=assume_associative,
                                    names=names,
@@ -98,16 +98,16 @@ class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclide
                  field,
                  mult_table,
                  rank,
-                 eja_basis,
+                 superalgebra_basis,
                  vector_space,
                  assume_associative=True,
                  names='f',
                  category=None,
                  natural_basis=None):
 
-        self._superalgebra = eja_basis[0].parent()
+        self._superalgebra = superalgebra_basis[0].parent()
         self._vector_space = vector_space
-        self._eja_basis = eja_basis
+        self._superalgebra_basis = superalgebra_basis
 
         fdeja = super(FiniteDimensionalEuclideanJordanElementSubalgebra, self)
         fdeja.__init__(field,
@@ -119,6 +119,13 @@ class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclide
                        natural_basis=natural_basis)
 
 
+    def superalgebra(self):
+        """
+        Return the superalgebra that this algebra was generated from.
+        """
+        return self._superalgebra
+
+
     def vector_space(self):
         """
         SETUP::
@@ -167,7 +174,7 @@ class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclide
             ::
 
             """
-            if elt in A._superalgebra:
+            if elt in A.superalgebra():
                     # Try to convert a parent algebra element into a
                     # subalgebra element...
                 try:
@@ -180,3 +187,43 @@ class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclide
             FiniteDimensionalEuclideanJordanAlgebraElement.__init__(self,
                                                                     A,
                                                                     elt)
+
+        def superalgebra_element(self):
+            """
+            Return the object in our algebra's superalgebra that corresponds
+            to myself.
+
+            SETUP::
+
+                sage: from mjo.eja.eja_algebra import (RealSymmetricEJA,
+                ....:                                  random_eja)
+
+            EXAMPLES::
+
+                sage: J = RealSymmetricEJA(3)
+                sage: x = sum(J.gens())
+                sage: x
+                e0 + e1 + e2 + e3 + e4 + e5
+                sage: A = x.subalgebra_generated_by()
+                sage: A(x)
+                f1
+                sage: A(x).superalgebra_element()
+                e0 + e1 + e2 + e3 + e4 + e5
+
+            TESTS:
+
+            We can convert back and forth faithfully::
+
+                sage: set_random_seed()
+                sage: J = random_eja()
+                sage: x = J.random_element()
+                sage: A = x.subalgebra_generated_by()
+                sage: A(x).superalgebra_element() == x
+                True
+                sage: y = A.random_element()
+                sage: A(y.superalgebra_element()) == y
+                True
+
+            """
+            return self.parent().superalgebra().linear_combination(
+              zip(self.vector(), self.parent()._superalgebra_basis) )