eja: fix the subalgebra generated by zero.

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

diff --git a/mjo/eja/eja_subalgebra.py b/mjo/eja/eja_subalgebra.py
index a3ad92a4f9f5acedc7a12c6c11971f0d9351c3a3..c82bd1a485c5eb6b82e92134fc30658be4d6d669 100644 (file)
--- a/mjo/eja/eja_subalgebra.py
+++ b/mjo/eja/eja_subalgebra.py
@@ -71,19 +71,81 @@ class FiniteDimensionalEuclideanJordanElementSubalgebraElement(FiniteDimensional
 class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclideanJordanAlgebra):
     """
     The subalgebra of an EJA generated by a single element.
+
+    SETUP::
+
+        sage: from mjo.eja.eja_algebra import (ComplexHermitianEJA,
+        ....:                                  JordanSpinEJA)
+
+    TESTS:
+
+    Ensure that our generator names don't conflict with the superalgebra::
+
+        sage: J = JordanSpinEJA(3)
+        sage: J.one().subalgebra_generated_by().gens()
+        (f0,)
+        sage: J = JordanSpinEJA(3, prefix='f')
+        sage: J.one().subalgebra_generated_by().gens()
+        (g0,)
+        sage: J = JordanSpinEJA(3, prefix='b')
+        sage: J.one().subalgebra_generated_by().gens()
+        (c0,)
+
+    Ensure that we can find subalgebras of subalgebras::
+
+        sage: A = ComplexHermitianEJA(3).one().subalgebra_generated_by()
+        sage: B = A.one().subalgebra_generated_by()
+        sage: B.dimension()
+        1
+
     """
     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()]
-        basis_vectors = [superalgebra.one().to_vector()]
+        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(self._superalgebra.one().to_vector())]
         W = V.span_of_basis(basis_vectors)
         for exponent in range(1, V.dimension()):
             new_power = elt**exponent
-            basis_vectors.append( new_power.to_vector() )
+            basis_vectors.append( V.from_vector(new_power.to_vector()) )
             try:
                 W = V.span_of_basis(basis_vectors)
                 superalgebra_basis.append( new_power )
@@ -98,16 +160,17 @@ 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):
             for j in range(n):
                 product = superalgebra_basis[i]*superalgebra_basis[j]
-                mult_table[i][j] = W.coordinate_vector(product.to_vector())
-
-        # TODO: We'll have to redo this and make it unique again...
-        prefix = 'f'
+                # product.to_vector() might live in a vector subspace
+                # if our parent algebra is already a subalgebra. We
+                # use V.from_vector() to make it "the right size" in
+                # that case.
+                product_vector = V.from_vector(product.to_vector())
+                mult_table[i][j] = W.coordinate_vector(product_vector)
 
         # The rank is the highest possible degree of a minimal
         # polynomial, and is bounded above by the dimension. We know
@@ -117,11 +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
 
@@ -221,7 +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):