eja: fix inclusions/projections with trivial algebras.

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

diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py
index 2bf7aa2743d1fefc6952e521d17cb1f3d22fa276..739bff334c5aa2069dbf09244e7a7fa39ceaccb3 100644 (file)
--- a/mjo/eja/eja_element.py
+++ b/mjo/eja/eja_element.py
@@ -523,6 +523,11 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
         whether or not the paren't algebra's zero element is a root
         of this element's minimal polynomial.
 
         whether or not the paren't algebra's zero element is a root
         of this element's minimal polynomial.
 

+        That is... unless the coefficients of our algebra's
+        "characteristic polynomial of" function are already cached!
+        In that case, we just use the determinant (which will be fast
+        as a result).
+

         Beware that we can't use the superclass method, because it
         relies on the algebra being associative.
 
         Beware that we can't use the superclass method, because it
         relies on the algebra being associative.
 


@@ -553,6 +558,11 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             else:
                 return False
 
             else:
                 return False
 

+        if self.parent()._charpoly_coefficients.is_in_cache():
+            # The determinant will be quicker than computing the minimal
+            # polynomial from scratch, most likely.
+            return (not self.det().is_zero())
+

         # In fact, we only need to know if the constant term is non-zero,
         # so we can pass in the field's zero element instead.
         zero = self.base_ring().zero()
         # In fact, we only need to know if the constant term is non-zero,
         # so we can pass in the field's zero element instead.
         zero = self.base_ring().zero()


@@ -1008,6 +1018,10 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
         """
         B = self.parent().natural_basis()
         W = self.parent().natural_basis_space()
         """
         B = self.parent().natural_basis()
         W = self.parent().natural_basis_space()

+
+        # This is just a manual "from_vector()", but of course
+        # matrix spaces aren't vector spaces in sage, so they
+        # don't have a from_vector() method.

         return W.linear_combination(zip(B,self.to_vector()))
 
 
         return W.linear_combination(zip(B,self.to_vector()))
 
 


@@ -1253,7 +1267,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             sage: (J0, J5, J1) = J.peirce_decomposition(c1)
             sage: (f0, f1, f2) = J1.gens()
             sage: f0.spectral_decomposition()
             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)]
+            [(0, f2), (1, f0)]

 
         """
         A = self.subalgebra_generated_by(orthonormalize_basis=True)
 
         """
         A = self.subalgebra_generated_by(orthonormalize_basis=True)