From: Michael Orlitzky <michael@orlitzky.com>
Date: Thu, 21 Feb 2019 01:32:23 +0000 (-0500)
Subject: mjo/polynomial.py: add another multidiv test based on an exercise.
X-Git-Url: https://gitweb.michael.orlitzky.com/?a=commitdiff_plain;h=deb1e9c381606b637dac0f8948703fb4c27502b5;p=sage.d.git

mjo/polynomial.py: add another multidiv test based on an exercise.
---

diff --git a/mjo/polynomial.py b/mjo/polynomial.py
index 2b8dc2a..ca09ebe 100644
--- a/mjo/polynomial.py
+++ b/mjo/polynomial.py
@@ -162,6 +162,19 @@ def multidiv(f, gs):
         ....:                     for g in gs ))
         True
 
+    Exercise 8 in Section 2.4 of Cox, Little, and O'Shea says that we
+    should always get a zero remainder if we divide an element of a
+    monomial ideal by its generators::
+
+        sage: set_random_seed()
+        sage: R = PolynomialRing(QQ,'x,y,z')
+        sage: gs = R.random_element().monomials()
+        sage: I = R.ideal(gs)
+        sage: f = I.random_element(ZZ.random_element(5).abs())
+        sage: (qs, r) = multidiv(f, gs)
+        sage: r.is_zero()
+        True
+
     """
     R = f.parent()
     s = len(gs)