homalg swMATH ID: 411 Software Authors: Barakat, Mohamed; Robertz, Daniel Description: homalg: a meta-package for homological algebra. 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. Hom R , ⊗ R , Ext R i , Tor i R , 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 Homepage: http://homalg-project.github.io/ Source Code: https://github.com/homalg-project/homalg_project Programming Languages: GAP4 Dependencies: GAP Related Software: GAP; SINGULAR; Plural; Macaulay2; OreModules; SageMath; Magma; Janet; PurityFiltration; GeneralizedMorphismsForCAP; LinearAlgebraForCAP; ModulePresentationsForCAP; CAP; Maple; Letterplace; GitHub; Normaliz; OreMorphisms; LocalizeRingForHomalg; olga.lib Cited in: 29 Publications Further Publications: http://homalg.math.rwth-aachen.de/index.php/publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year homalg: a meta-package for homological algebra. Zbl 1151.13306Barakat, Mohamed; Robertz, Daniel 2008 all top 5 Cited by 33 Authors 9 Barakat, Mohamed 6 Robertz, Daniel 4 Levandovskyy, Viktor 4 Quadrat, Alban 3 Lange-Hegermann, Markus 3 Zeid, Karim Abou 2 García Sánchez, Pedro A. 2 Metzlaff, Tobias 2 Posur, Sebastian 1 Behrends, Reimer 1 Bies, Martin 1 Böhm, Janko 1 Cano, Guillaume 1 Cluzeau, Thomas 1 Cohen, Cyril 1 Cuntz, Michael Joachim 1 Decker, Wolfram 1 Delgado, Manuel 1 Dénès, Maxime 1 Effenberger, Felix 1 Heinle, Albert 1 Jefferson, Christopher 1 Keicher, Simon 1 Kühne, Lukas 1 Leuner, Martin 1 Mayrhofer, Christoph 1 Mörtberg, Anders 1 Napp, Diego 1 Ren, Yue 1 Schönemann, Hans 1 Siles, Vincent 1 Spreer, Jonathan 1 Weigand, Timo all top 5 Cited in 15 Serials 4 ACM Communications in Computer Algebra 2 Acta Applicandae Mathematicae 2 Journal of Symbolic Computation 2 Multidimensional Systems and Signal Processing 2 Journal of Algebra and its Applications 1 Advances in Mathematics 1 Archiv der Mathematik 1 Journal of Algebra 1 SIAM Journal on Discrete Mathematics 1 MCSS. Mathematics of Control, Signals, and Systems 1 Linear Algebra and its Applications 1 Applied Categorical Structures 1 Journal of High Energy Physics 1 Lecture Notes in Mathematics 1 Logical Methods in Computer Science all top 5 Cited in 17 Fields 16 Computer science (68-XX) 10 Associative rings and algebras (16-XX) 9 Commutative algebra (13-XX) 4 Category theory; homological algebra (18-XX) 4 Several complex variables and analytic spaces (32-XX) 4 Systems theory; control (93-XX) 3 Partial differential equations (35-XX) 2 Combinatorics (05-XX) 2 Field theory and polynomials (12-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Group theory and generalizations (20-XX) 2 Convex and discrete geometry (52-XX) 1 Algebraic geometry (14-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX) 1 Numerical analysis (65-XX) 1 Quantum theory (81-XX) Citations by Year