From: Michael Orlitzky <michael@orlitzky.com>
Date: Wed, 25 Nov 2020 04:43:17 +0000 (-0500)
Subject: eja: use cached charpoly for element inverse() if possible.
X-Git-Url: https://gitweb.michael.orlitzky.com/?a=commitdiff_plain;h=0b151420d2a7cfc0b0af812f2204eeda4b9a70ba;p=sage.d.git

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

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index 3c63d3b..87cdcbc 100644
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -30,9 +30,7 @@
    the usual one. Then for the basis to be orthonormal, we would need
    to divide e.g. (1,0,0) by <(1,0,0),(1,0,0)> = 2 to normalize it.
 
-8. Use charpoly for inverse itself?
+8. Pre-cache charpoly for some small algebras?
 
-9. Pre-cache charpoly for some small algebras?
-
-10. Compute the scalar in the general natural_inner_product() for
-    matrices, so no overrides are necessary.
\ No newline at end of file
+9. Compute the scalar in the general natural_inner_product() for
+   matrices, so no overrides are necessary.
\ No newline at end of file
diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py
index 739bff3..5a0b213 100644
--- 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)