From: Michael Orlitzky <michael@orlitzky.com>
Date: Mon, 23 Nov 2020 03:39:59 +0000 (-0500)
Subject: eja: use cached charpoly for element inverse when available.
X-Git-Url: http://gitweb.michael.orlitzky.com/?p=sage.d.git;a=commitdiff_plain;h=f02d09e53017ba3b3b5592a45be84487c580379d

eja: use cached charpoly for element inverse when available.
---

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index 220a701..94fb172 100644
--- 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 a5880c4..739bff3 100644
--- 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()