homalg

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


References in zbMATH (referenced in 24 articles , 1 standard article )

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  1. Janko Boehm, Wolfram Decker, Simon Keicher, Yue Ren: Current Challenges in Developing Open Source Computer Algebra Systems (2017) arXiv
  2. Böhm, Janko; Decker, Wolfram; Keicher, Simon; Ren, Yue: Current challenges in developing open source computer algebra systems (2016)
  3. Cano, Guillaume; Cohen, Cyril; Dénès, Maxime; Mörtberg, Anders; Siles, Vincent: Formalized linear algebra over elementary divisor rings in Coq (2016)
  4. Delgado, M.; García-Sánchez, P.A.: numericalsgps, a GAP package for numerical semigroups (2016)
  5. García-Sánchez, P.A.: An overview of the computational aspects of nonunique factorization invariants (2016)
  6. Barakat, Mohamed: On subdirect factors of a projective module and applications to system theory. (2015)
  7. Heinle, Albert; Levandovskyy, Viktor: The SDEval benchmarking toolkit (2015)
  8. Robertz, Daniel: Recent progress in an algebraic analysis approach to linear systems (2015)
  9. Barakat, Mohamed; Lange-Hegermann, Markus: On the ext-computability of Serre quotient categories (2014)
  10. Quadrat, A.; Robertz, D.: A constructive study of the module structure of rings of partial differential operators. (2014)
  11. Robertz, Daniel: Formal algorithmic elimination for PDEs (2014)
  12. Quadrat, Alban: Grade filtration of linear functional systems. (2013)
  13. Barakat, Mohamed; Cuntz, Michael: Coxeter and crystallographic arrangements are inductively free (2012)
  14. Barakat, Mohamed; Lange-Hegermann, Markus: The homalg project (2012) MathEduc
  15. Barakat, Mohamed; Lange-Hegermann, Markus: An axiomatic setup for algorithmic homological algebra and an alternative approach to localization (2011)
  16. Effenberger, Felix; Spreer, Jonathan: Simplicial blowups and discrete normal surfaces in \ssfsimpcomp (2011)
  17. Barakat, Mohamed: Purity filtration and the fine structure of autonomy. (2010)
  18. Barakat, Mohamed; Lange-Hegermann, Markus: LocalizeRingForHomalg: localize commutative rings at maximal ideals (2010)
  19. Quadrat, Alban: Purity filtration of 2-dimensional linear systems. (2010)
  20. Barakat, Mohamed; Robertz, Daniel: conley: Computing connection matrices in Maple (2009)

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Further publications can be found at: http://homalg.math.rwth-aachen.de/index.php/publications