eja: fix the natural representation in trivial subalgebras.

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

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index 832e7a19d5857fcd429a11b8693565aa781ba617..42b2474d6971d81c8a1fcda67b079892a3e8af25 100644 (file)
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -9,10 +9,11 @@ from sage.algebras.quatalg.quaternion_algebra import QuaternionAlgebra
 from sage.categories.magmatic_algebras import MagmaticAlgebras
 from sage.combinat.free_module import CombinatorialFreeModule
 from sage.matrix.constructor import matrix
+from sage.matrix.matrix_space import MatrixSpace
 from sage.misc.cachefunc import cached_method
 from sage.misc.prandom import choice
 from sage.misc.table import table
-from sage.modules.free_module import VectorSpace
+from sage.modules.free_module import FreeModule, VectorSpace
 from sage.rings.integer_ring import ZZ
 from sage.rings.number_field.number_field import QuadraticField
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
@@ -207,8 +208,13 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule):
         determinant).
         """
         z = self._a_regular_element()
-        V = self.vector_space()
-        V1 = V.span_of_basis( (z**k).to_vector() for k in range(self.rank()) )
+        # Don't use the parent vector space directly here in case this
+        # happens to be a subalgebra. In that case, we would be e.g.
+        # two-dimensional but span_of_basis() would expect three
+        # coordinates.
+        V = VectorSpace(self.base_ring(), self.vector_space().dimension())
+        basis = [ (z**k).to_vector() for k in range(self.rank()) ]
+        V1 = V.span_of_basis( basis )
         b =  (V1.basis() + V1.complement().basis())
         return V.span_of_basis(b)
 
@@ -263,7 +269,13 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule):
         # have multivatiate polynomial entries.
         names = tuple('X' + str(i) for i in range(1,n+1))
         R = PolynomialRing(self.base_ring(), names)
-        V = self.vector_space().change_ring(R)
+
+        # Using change_ring() on the parent's vector space doesn't work
+        # here because, in a subalgebra, that vector space has a basis
+        # and change_ring() tries to bring the basis along with it. And
+        # that doesn't work unless the new ring is a PID, which it usually
+        # won't be.
+        V = FreeModule(R,n)
 
         # Now let x = (X1,X2,...,Xn) be the vector whose entries are
         # indeterminates...
@@ -503,11 +515,23 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule):
 
         """
         if self._natural_basis is None:
-            return tuple( b.to_vector().column() for b in self.basis() )
+            M = self.natural_basis_space()
+            return tuple( M(b.to_vector()) for b in self.basis() )
         else:
             return self._natural_basis
 
 
+    def natural_basis_space(self):
+        """
+        Return the matrix space in which this algebra's natural basis
+        elements live.
+        """
+        if self._natural_basis is None or len(self._natural_basis) == 0:
+            return MatrixSpace(self.base_ring(), self.dimension(), 1)
+        else:
+            return self._natural_basis[0].matrix_space()
+
+
     @cached_method
     def one(self):
         """