X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;ds=sidebyside;f=mjo%2Feja%2Feja_algebra.py;h=06f6f531ac46305da59ec2b4290ba808602cea50;hb=0fd07263cc543e345f3cd7668938f8a0de70641f;hp=580c923c37a7c00ed492272161eec70ced95c2de;hpb=ce4c7e206125cd399239698d26f951a4aac073f2;p=sage.d.git

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index 580c923..06f6f53 100644
--- 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...
@@ -404,6 +415,29 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule):
         return x.trace_inner_product(y)
 
 
+    def is_trivial(self):
+        """
+        Return whether or not this algebra is trivial.
+
+        A trivial algebra contains only the zero element.
+
+        SETUP::
+
+            sage: from mjo.eja.eja_algebra import ComplexHermitianEJA
+
+        EXAMPLES::
+
+            sage: J = ComplexHermitianEJA(3)
+            sage: J.is_trivial()
+            False
+            sage: A = J.zero().subalgebra_generated_by()
+            sage: A.is_trivial()
+            True
+
+        """
+        return self.dimension() == 0
+
+
     def multiplication_table(self):
         """
         Return a visual representation of this algebra's multiplication
@@ -546,6 +580,15 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule):
         return self.linear_combination(zip(self.gens(), coeffs))
 
 
+    def random_element(self):
+        # Temporary workaround for https://trac.sagemath.org/ticket/28327
+        if self.is_trivial():
+            return self.zero()
+        else:
+            s = super(FiniteDimensionalEuclideanJordanAlgebra, self)
+            return s.random_element()
+
+
     def rank(self):
         """
         Return the rank of this EJA.