From: Michael Orlitzky <michael@orlitzky.com>
Date: Mon, 1 Mar 2021 04:28:55 +0000 (-0500)
Subject: eja: speed up minimal_polynomial(), in theory.
X-Git-Url: https://gitweb.michael.orlitzky.com/?a=commitdiff_plain;h=827b203e50561de19857935f456509cf2392ee70;p=sage.d.git

eja: speed up minimal_polynomial(), in theory.
---

diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py
index 81c2b54..52933e2 100644
--- a/mjo/eja/eja_element.py
+++ b/mjo/eja/eja_element.py
@@ -1047,19 +1047,30 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
 
         """
         if self.is_zero():
-            # We would generate a zero-dimensional subalgebra
-            # where the minimal polynomial would be constant.
-            # That might be correct, but only if *this* algebra
-            # is trivial too.
-            if not self.parent().is_trivial():
-                # Pretty sure we know what the minimal polynomial of
-                # the zero operator is going to be. This ensures
-                # consistency of e.g. the polynomial variable returned
-                # in the "normal" case without us having to think about it.
-                return self.operator().minimal_polynomial()
-
+            # Pretty sure we know what the minimal polynomial of
+            # the zero operator is going to be. This ensures
+            # consistency of e.g. the polynomial variable returned
+            # in the "normal" case without us having to think about it.
+            return self.operator().minimal_polynomial()
+
+        # If we don't orthonormalize the subalgebra's basis, then the
+        # first two monomials in the subalgebra will be self^0 and
+        # self^1... assuming that self^1 is not a scalar multiple of
+        # self^0 (the unit element). We special case these to avoid
+        # having to solve a system to coerce self into the subalgebra.
         A = self.subalgebra_generated_by(orthonormalize=False)
-        return A(self).operator().minimal_polynomial()
+
+        if A.dimension() == 1:
+            # Does a solve to find the scalar multiple alpha such that
+            # alpha*unit = self. We have to do this because the basis
+            # for the subalgebra will be [ self^0 ], and not [ self^1 ]!
+            unit = self.parent().one()
+            alpha = self.to_vector() / unit.to_vector()
+            return (unit.operator()*alpha).minimal_polynomial()
+        else:
+            # If the dimension of the subalgebra is >= 2, then we just
+            # use the second basis element.
+            return A.monomial(1).operator().minimal_polynomial()