eja: use cached charpoly for element inverse() if possible.

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

diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py
index 2bf7aa2743d1fefc6952e521d17cb1f3d22fa276..5a0b213296beaa301c1b891311cdba65ce98534f 100644 (file)
--- a/mjo/eja/eja_element.py
+++ b/mjo/eja/eja_element.py
@@ -507,6 +507,14 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
         if not self.is_invertible():
             raise ValueError("element is not invertible")
 
+        if self.parent()._charpoly_coefficients.is_in_cache():
+            # We can invert using our charpoly if it will be fast to
+            # compute. If the coefficients are cached, our rank had
+            # better be too!
+            r = self.parent().rank()
+            a = self.characteristic_polynomial().coefficients(sparse=False)
+            return (-1)**(r+1)*sum(a[i+1]*self**i for i in range(r))/self.det()
+
         return (~self.quadratic_representation())(self)
 
 
@@ -523,6 +531,11 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
         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.
 
@@ -553,6 +566,11 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             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()
@@ -1008,6 +1026,10 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
         """
         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()))
 
 
@@ -1253,7 +1275,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             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)