suggestion for documentation of Multivariate Polynomials

edit

The dependence of the ring on the term ordering is explained in

Gert-Martin Greuel, Gerhard Pfister "A Singular Introduction to Commutative Algebra" with contributions by Olaf Bachmann, Christoph Lossen and Hans Schoenemann Second, Extended Edition Springer-Verlag

Section 1.2 Monomial Orderings p. 16 "SINGULAR Example 1.2.13 (monomial orderings). Global orderings are denoted with a p at the end, referring to “polynomial ring” while local orderings end with an s, referring to “series ring”. "

Section 1.5 Rings Associated to Monomial Orderings p. 38 In this section we show that non–global monomial orderings lead to new rings which are localizations of the polynomial ring.

p. 39 Definition 1.5.1. For any monomial ordering > on Mon(x1,...,xn), we define K[x]> the localization of K[x]

I suggest adding a paragraph in Sage 9.1 Reference Manual: Polynomials, section 1.1 Constructors for Polynomial Rings, immediately after the first paragraph.

But I am singularly unqualified to write the paragraph. I barely grasp the meaning of "localization". I'm only suggesting this revision because I got into trouble because I was ignorant of the fact that "Constructors for polynomial rings" does not mean "Constructors of polynomial rings".