eja: fix the subalgebra generated by zero.

diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py
index 287a217e785ff3e44109d3fc8d8fd85ed1ca4771..97c048dceb3e299e7a36ac1a15767ebb33af8fad 100644 (file)
--- a/mjo/eja/eja_element.py
+++ b/mjo/eja/eja_element.py
@@ -964,6 +964,15 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             sage: A(x^2) == A(x)*A(x)
             True
 
+        The subalgebra generated by the zero element is trivial::
+
+            sage: set_random_seed()
+            sage: A = random_eja().zero().subalgebra_generated_by()
+            sage: A
+            Euclidean Jordan algebra of dimension 0 over Rational Field
+            sage: A.one()
+            0
+
         """
         return FiniteDimensionalEuclideanJordanElementSubalgebra(self)
 

diff --git a/mjo/eja/eja_subalgebra.py b/mjo/eja/eja_subalgebra.py
index 9e5b010145b99f9442b5a86df8db3cd7d25048ad..c82bd1a485c5eb6b82e92134fc30658be4d6d669 100644 (file)
--- a/mjo/eja/eja_subalgebra.py
+++ b/mjo/eja/eja_subalgebra.py
@@ -100,16 +100,48 @@ class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclide
 
     """
     def __init__(self, elt):
-        superalgebra = elt.parent()
+        self._superalgebra = elt.parent()
+        category = self._superalgebra.category().Associative()
+        V = self._superalgebra.vector_space()
+        field = self._superalgebra.base_ring()
+
+        # A half-assed attempt to ensure that we don't collide with
+        # the superalgebra's prefix (ignoring the fact that there
+        # could be super-superelgrbas in scope). If possible, we
+        # 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' ]
+        try:
+            prefix = prefixen[prefixen.index(self._superalgebra.prefix()) + 1]
+        except ValueError:
+            prefix = prefixen[0]
+
+        if elt.is_zero():
+            # Short circuit because 0^0 == 1 is going to make us
+            # think we have a one-dimensional algebra otherwise.
+            natural_basis = tuple()
+            mult_table = tuple()
+            rank = 0
+            self._vector_space = V.zero_subspace()
+            self._superalgebra_basis = []
+            fdeja = super(FiniteDimensionalEuclideanJordanElementSubalgebra,
+                          self)
+            return fdeja.__init__(field,
+                                  mult_table,
+                                  rank,
+                                  prefix=prefix,
+                                  category=category,
+                                  natural_basis=natural_basis)
+
 
         # First compute the vector subspace spanned by the powers of
         # the given element.
-        V = superalgebra.vector_space()
-        superalgebra_basis = [superalgebra.one()]
+        superalgebra_basis = [self._superalgebra.one()]
         # If our superalgebra is a subalgebra of something else, then
         # superalgebra.one().to_vector() won't have the right
         # coordinates unless we use V.from_vector() below.
-        basis_vectors = [V.from_vector(superalgebra.one().to_vector())]
+        basis_vectors = [V.from_vector(self._superalgebra.one().to_vector())]
         W = V.span_of_basis(basis_vectors)
         for exponent in range(1, V.dimension()):
             new_power = elt**exponent
@@ -128,7 +160,6 @@ class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclide
         # Now figure out the entries of the right-multiplication
         # matrix for the successive basis elements b0, b1,... of
         # that subspace.
-        field = superalgebra.base_ring()
         n = len(superalgebra_basis)
         mult_table = [[W.zero() for i in range(n)] for j in range(n)]
         for i in range(n):
@@ -141,18 +172,6 @@ class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclide
                 product_vector = V.from_vector(product.to_vector())
                 mult_table[i][j] = W.coordinate_vector(product_vector)
 
-        # A half-assed attempt to ensure that we don't collide with
-        # the superalgebra's prefix (ignoring the fact that there
-        # could be super-superelgrbas in scope). If possible, we
-        # 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' ]
-        try:
-            prefix = prefixen[prefixen.index(superalgebra.prefix()) + 1]
-        except ValueError:
-            prefix = prefixen[0]
-
         # The rank is the highest possible degree of a minimal
         # polynomial, and is bounded above by the dimension. We know
         # in this case that there's an element whose minimal
@@ -161,11 +180,10 @@ class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclide
         # its rank too.
         rank = W.dimension()
 
-        category = superalgebra.category().Associative()
         natural_basis = tuple( b.natural_representation()
                                for b in superalgebra_basis )
 
-        self._superalgebra = superalgebra
+
         self._vector_space = W
         self._superalgebra_basis = superalgebra_basis
 
@@ -265,7 +283,10 @@ class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclide
             sage: actual == expected
             True
         """
-        return self.monomial(self.one_basis())
+        if self.dimension() == 0:
+            return self.zero()
+        else:
+            return self.monomial(self.one_basis())
 
 
     def superalgebra(self):