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