Reference Manual

Reference Manual

This section is intended to offer detailed documentation on every aspect of the system of interest to users. We organize the software and therefore the documentation primarily according to the types of objects, and secondarily according to the functions available for dealing with objects of a given type. For example, if you want to know how to get a projective resolution of an ideal, you should first find either the section dealing with ideals or the section dealing with chain complexes. More briefly, look first for the noun and then for the verb.

In line with that advice, we list here some types of things with particular mathematical interest.

Ring -- the class of all rings

Ideal -- the class of all ideals

Matrix -- the class of all matrices

Module -- the class of all modules

RingMap -- the class of all ring maps

GroebnerBasis -- the class of all Groebner bases

ChainComplex -- the class of all chain complexes

Variety -- the class of all algebraic varieties

Some types of things of interest to the programmer and user:

Function -- the class of all functions

VisibleList -- the class of all visible lists

File -- the class of all files

A list of the operators:

operators -- an overview

We've mentioned that our software is organized according to the types of things there are. The types form a hierarchy; for example, a polynomial ring is a type of ring, and an affine variety is a type of variety. At the top of the hierarchy sits Thing; everything is a thing, and every type is a type of thing. The documentation is organized here as a view of the hierarchy from the top down, so you can find everything (eventually) in the following section, its subsections, or the sections it refers to.

Thing -- the class of all things