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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: SINGULAR; GAP; Plural; Macaulay2; OreModules; CAP; GeneralizedMorphismsForCAP; ModulePresentationsForCAP; LinearAlgebraForCAP; SageMath; Magma; GitHub; PurityFiltration; Maple; Janet; ZariskiFrames; LocalizeRingForHomalg; Letterplace; Normaliz; OreMorphisms
Cited in: 32 Documents
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 1151.13306
Barakat, Mohamed; Robertz, Daniel
2008
all top 5

Cited by 37 Authors

11 Barakat, Mohamed
6 Robertz, Daniel
4 Lange-Hegermann, Markus
4 Levandovskyy, Viktor
4 Quadrat, Alban
3 Zeid, Karim Abou
2 García Sánchez, Pedro A.
2 Kühne, Lukas
2 Metzlaff, Tobias
2 Posur, Sebastian
1 Behrends, Reimer
1 Bies, Martin
1 Böhm, Janko
1 Brüser, Robin
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 Fieker, Claus
1 Heinle, Albert
1 Huber, Tobias
1 Jefferson, Christopher
1 Keicher, Simon
1 Leuner, Martin
1 Mayrhofer, Christoph
1 Mörtberg, Anders
1 Napp, Diego
1 Piclum, Jan H.
1 Ren, Yue
1 Schönemann, Hans
1 Siles, Vincent
1 Spreer, Jonathan
1 Weigand, Timo
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Cited in 16 Serials

4 ACM Communications in Computer Algebra
2 Mathematics of Computation
2 Acta Applicandae Mathematicae
2 Journal of Symbolic Computation
2 Multidimensional Systems and Signal Processing
2 Journal of High Energy Physics
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 Lecture Notes in Mathematics
1 Logical Methods in Computer Science
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Cited in 17 Fields

16 Computer science (68-XX)
12 Commutative algebra (13-XX)
11 Associative rings and algebras (16-XX)
5 Several complex variables and analytic spaces (32-XX)
4 Algebraic geometry (14-XX)
4 Category theory; homological algebra (18-XX)
4 Systems theory; control (93-XX)
3 Combinatorics (05-XX)
3 Partial differential equations (35-XX)
3 Convex and discrete geometry (52-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 Quantum theory (81-XX)
1 Algebraic topology (55-XX)
1 Manifolds and cell complexes (57-XX)
1 Numerical analysis (65-XX)

Citations by Year