homalg – A META-PACKAGE FOR HOMOLOGICAL ALGEBRA

Author:

BARAKAT MOHAMED1,ROBERTZ DANIEL1

Affiliation:

1. Lehrstuhl B für Mathematik, RWTH-Aachen University, Templergraben 64, Aachen, 52062, Germany

Abstract

The central notion of this work is that of a functor between categories of finitely presented modules over so-called computable rings, i.e. rings R where one can algorithmically solve inhomogeneous linear equations with coefficients in R. The paper describes a way allowing one to realize such functors, e.g. HomR, ⊗R, [Formula: see text], [Formula: see text], as a mathematical object in a computer algebra system. Once this is achieved, one can compose and derive functors and even iterate this process without the need of any specific knowledge of these functors. These ideas are realized in the ring independent package homalg. It is designed to extend any computer algebra software implementing the arithmetics of a computable ring R, as soon as the latter contains algorithms to solve inhomogeneous linear equations with coefficients in R. Beside explaining how this suffices, the paper describes the nature of the extensions provided by homalg.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

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