Overview of the &MatricesForHomalg; Package Source Code
Rings, Ring Maps, Matrices, Ring Relations

The &MatricesForHomalg; package files
Filename .gd/.gi
Content
homalg
definitions of the basic &GAP4; categories
and some tool functions (e.g. homalgMode)
homalgTable
dictionaries between &MatricesForHomalg;
and the computing engines
HomalgRing
internal and external rings
HomalgRingMap
ring maps
HomalgMatrix
internal and external matrices
HomalgRingRelations
a set of ring relations

The Low Level Algorithms

In the following CAS or CASystem mean computer algebra systems.

The &MatricesForHomalg; package files (continued)
Filename .gd/.gi
Content
Tools
the elementary matrix operations that can be
overwritten using the homalgTable
(and hence delegable even to other CASystems)
Service
the three operations: basis, reduction, and syzygies;
they can also be overwritten using the homalgTable
(and hence delegable even to other CASystems)
Basic
higher level operations for matrices
(cannot be overwritten using the homalgTable)

Logical Implications for &MatricesForHomalg; Objects

The &MatricesForHomalg; package files (continued)
Filename .gd/.gi
Content
LIRNG
logical implications for rings
LIMAP
logical implications for ring maps
LIMAT
logical implications for matrices
COLEM
clever operations for lazy evaluated matrices

The subpackage &ResidueClassRingForHomalg;

The &MatricesForHomalg; package files (continued)
Filename .gd/.gi
Content
ResidueClassRingForHomalg
some global variables
ResidueClassRing
residue class rings, their elements, and matrices,
together with their constructors and operations
ResidueClassRingTools
the elementary matrix operations for matrices
over residue class rings
ResidueClassRingBasic
the three operations: basis, reduction, and syzygies
for matrices over residue class rings

The homalgTable for &GAP4; built-in rings

For the purposes of &homalg;, the ring of integers is, at least up till now, the only ring which is properly supported in &GAP4;. The &GAP4; built-in cababilities for polynomial rings (also univariate) and group rings do not statisfy the minimum requirements of &homalg;. The &GAP4; package &Gauss; enables &GAP; to fullfil the &homalg; requirements for prime fields, and &ZZ; / p^n.

The &MatricesForHomalg; package files (continued)
Filename .gi
Content
Integers
the homalgTable for the ring of integers