eja: refactor and fix the fast charpoly stuff that I broke recently.

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index 89b4d329b76d848c0caf1528c1c78b7faec1ff9a..849757608ba571aad69b1b6b84812cefafb34c2c 100644 (file)
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -9,9 +9,6 @@
 5. Factor out the unit-norm basis (and operator symmetry) tests once
    all of the algebras pass.
 
-6. Refactor the current ungodly fast charpoly hack (relies on the
-   theory to ensure that the charpolys are equal.)
+6. Implement random_instance() for the main EJA class.
 
-7. Implement random_instance() for the main EJA class.
-
-8. Implement random_instance() for the subalgebra class.
+7. Implement random_instance() for the subalgebra class.

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index 80147dfa62ca0ab408d6da2f5a7ee047eb788f05..2a5e624cf4730e8296373d5fe542bbc78d31666e 100644 (file)
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -61,9 +61,6 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule):
         self._rank = rank
         self._natural_basis = natural_basis
 
-        # TODO: HACK for the charpoly.. needs redesign badly.
-        self._basis_normalizers = None
-
         if category is None:
             category = MagmaticAlgebras(field).FiniteDimensional()
             category = category.WithBasis().Unital()
@@ -259,19 +256,6 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule):
         store the trace/determinant (a_{r-1} and a_{0} respectively)
         separate from the entire characteristic polynomial.
         """
-        if self._basis_normalizers is not None:
-             # Must be a matrix class?
-             # WARNING/TODO: this whole mess is mis-designed.
-             n = self.natural_basis_space().nrows()
-             field = self.base_ring().base_ring() # yeeeeaaaahhh
-             J = self.__class__(n, field, False)
-             (_,x,_,_) = J._charpoly_matrix_system()
-             p = J._charpoly_coeff(i)
-             # p might be missing some vars, have to substitute "optionally"
-             pairs = zip(x.base_ring().gens(), self._basis_normalizers)
-             substitutions = { v: v*c for (v,c) in pairs }
-             return p.subs(substitutions)
-
         (A_of_x, x, xr, detA) = self._charpoly_matrix_system()
         R = A_of_x.base_ring()
         if i >= self.rank():
@@ -908,6 +892,9 @@ class MatrixEuclideanJordanAlgebra(FiniteDimensionalEuclideanJordanAlgebra):
     def __init__(self, n, field=QQ, normalize_basis=True, **kwargs):
         S = self._denormalized_basis(n, field)
 
+        # Used in this class's fast _charpoly_coeff() override.
+        self._basis_normalizers = None
+
         if n > 1 and normalize_basis:
             # We'll need sqrt(2) to normalize the basis, and this
             # winds up in the multiplication table, so the whole
@@ -932,6 +919,28 @@ class MatrixEuclideanJordanAlgebra(FiniteDimensionalEuclideanJordanAlgebra):
                               **kwargs)
 
 
+    @cached_method
+    def _charpoly_coeff(self, i):
+        """
+        Override the parent method with something that tries to compute
+        over a faster (non-extension) field.
+        """
+        if self._basis_normalizers is None:
+            # We didn't normalize, so assume that the basis we started
+            # with had entries in a nice field.
+            return super(MatrixEuclideanJordanAlgebra, self)._charpoly_coeff(i)
+        else:
+            n = self.natural_basis_space().nrows()
+            field = self.base_ring().base_ring() # yeeeeaaaahhh
+            J = self.__class__(n, field, False)
+            (_,x,_,_) = J._charpoly_matrix_system()
+            p = J._charpoly_coeff(i)
+            # p might be missing some vars, have to substitute "optionally"
+            pairs = zip(x.base_ring().gens(), self._basis_normalizers)
+            substitutions = { v: v*c for (v,c) in pairs }
+            return p.subs(substitutions)
+
+
     @staticmethod
     def multiplication_table_from_matrix_basis(basis):
         """