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4.8.1 Introduction to Rings
Polynomial rings play a central role in CoCoA. Indeed, every object
in CoCoA is defined over a base ring which is a polynomial ring. The
user can define many rings, but at any time a current ring
active within the system. Most commands use the current ring as the
Once a ring has been defined, the system can handle the following
mathematical objects defined over that ring:
* numbers (integers, rationals, modular integers);
* vectors of polynomials;
* rational functions;
* modules (submodules of a free module);
* lists of objects;
* matrices of objects.
Variables containing ring-dependent objects such as polynomials,
ideals, and modules are labeled
by their ring. Variables
containing objects such as integers which are not dependent on a
particular ring are not labeled.
IMPORTANT NOTE: Starting with CoCoA 3.5, variables are no longer local
to specific rings, i.e., all variables are accessible from all rings.
The next sections explains how to create a ring.