eja: start experiment full_spectral_decomposition() method.

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

diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py
index 1cf93cce6127b476796cdc130bfd98cfb7f21e41..2976a38f91a986b7e5f2fafd7a24560d29411755 100644 (file)
--- a/mjo/eja/eja_element.py
+++ b/mjo/eja/eja_element.py
@@ -1220,6 +1220,17 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             sage: l0*c0 + l1*c1 == x
             True
 
+        The spectral decomposition should work in subalgebras, too::
+
+            sage: J = RealSymmetricEJA(4)
+            sage: (e0, e1, e2, e3, e4, e5, e6, e7, e8, e9) = J.gens()
+            sage: A = 2*e5 - 2*e8
+            sage: (lambda1, c1) = A.spectral_decomposition()[1]
+            sage: (J0, J5, J1) = J.peirce_decomposition(c1)
+            sage: (f0, f1, f2) = J1.gens()
+            sage: f0.spectral_decomposition()
+            [(0, 1.000000000000000?*f2), (1, 1.000000000000000?*f0)]
+
         """
         A = self.subalgebra_generated_by(orthonormalize_basis=True)
         result = []
@@ -1227,6 +1238,37 @@ 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