eja: use cached charpoly for element inverse when available.

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index 220a70193014f215b25758fe39f42c82e1fbfbc4..94fb172aba0dda1d601e7c70ccf4f991749a6fcc 100644 (file)
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -21,9 +21,7 @@
    This may require supporting "basis" as a list of basis vectors
    (as opposed to superalgebra elements) in the subalgebra constructor.
 
-7. Use charpoly for inverse stuff if it's cached.
-
-8. The inner product should be an *argument* to the main EJA
+7. The inner product should be an *argument* to the main EJA
    constructor.  Afterwards, the basis normalization step should be
    optional (and enabled by default) for ALL algebras, since any
    algebra can have a nonstandard inner-product and its basis can be

diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py
index a5880c4c4c3fc083726fbf2adcef6ee071e7cd63..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.
 
+        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 +558,11 @@ 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()