eja: fix the characteristic polynomial in 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..06f6f531ac46305da59ec2b4290ba808602cea50 100644 (file)
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -12,7 +12,7 @@ from sage.matrix.constructor import matrix
 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 +207,13 @@ 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 +268,13 @@ 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...