sage: set_random_seed()
sage: R = PolynomialRing(QQ, 'x,y,z')
- sage: x,y,z = R.gens()
sage: s = ZZ.random_element(1,5).abs()
sage: gs = [ R.random_element() for idx in range(s) ]
sage: f = R.random_element(ZZ.random_element(10).abs())
....: 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)