eja: simplify and unify the charpoly/rank stuff.

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

diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py
index 2976a38f91a986b7e5f2fafd7a24560d29411755..926f2bf57a612c71eab53b693daa1e3f559ad6bc 100644 (file)
--- a/mjo/eja/eja_element.py
+++ b/mjo/eja/eja_element.py
@@ -386,11 +386,11 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
         """
         P = self.parent()
         r = P.rank()
-        p = P._charpoly_coeff(0)
-        # The _charpoly_coeff function already adds the factor of
-        # -1 to ensure that _charpoly_coeff(0) is really what
-        # appears in front of t^{0} in the charpoly. However,
-        # we want (-1)^r times THAT for the determinant.
+        p = P._charpoly_coefficients()[0]
+        # The _charpoly_coeff function already adds the factor of -1
+        # to ensure that _charpoly_coefficients()[0] is really what
+        # appears in front of t^{0} in the charpoly. However, we want
+        # (-1)^r times THAT for the determinant.
         return ((-1)**r)*p(*self.to_vector())
 
 
@@ -1238,37 +1238,6 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             result.append( (evalue, proj(A.one()).superalgebra_element()) )
         return result
 
-    def full_spectral_decomposition(self):
-        if self.is_zero():
-            # Following the convention that the empty sum is the
-            # algebra's additive identity.
-            return []
-
-        A = self.subalgebra_generated_by(orthonormalize_basis=True)
-        if A.dimension() == 1:
-            # I'm a scalar multiple of the identity element
-            s = self.norm() / A.one().norm()
-            return [(s, self * ~s)]
-
-        result = []
-        for (evalue, proj) in A(self).operator().spectral_decomposition():
-            c = proj(A.one()).superalgebra_element()
-
-            # We know that "c" here is idempotent, so the only question is
-            # whether or not it can be decomposed further.
-            if c.is_primitive_idempotent():
-                result.append( (evalue, c) )
-            else:
-                for b in A.gens():
-                    b_decomp = b.full_spectral_decomposition()
-                    if len(b_decomp) > 1:
-                        for (a,y) in b_decomp:
-                            y_sup = y.superalgebra_element()
-                            eigenvecs = [ r[1] for r in result ]
-                            if not y_sup in eigenvecs:
-                                result.append( ( evalue*a, y_sup) )
-        return result
-
     def subalgebra_generated_by(self, orthonormalize_basis=False):
         """
         Return the associative subalgebra of the parent EJA generated
@@ -1431,7 +1400,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             # the trace is an empty sum.
             return P.base_ring().zero()
 
-        p = P._charpoly_coeff(r-1)
+        p = P._charpoly_coefficients()[r-1]
         # The _charpoly_coeff function already adds the factor of
         # -1 to ensure that _charpoly_coeff(r-1) is really what
         # appears in front of t^{r-1} in the charpoly. However,