Macaulay2

Macaulay2 is a software system devoted to supporting research in algebraic geometry and commutative algebra, whose creation has been funded by the National Science Foundation since 1992. Macaulay2 includes core algorithms for computing Gröbner bases and graded or multi-graded free resolutions of modules over quotient rings of graded or multi-graded polynomial rings with a monomial ordering. The core algorithms are accessible through a versatile high level interpreted user language with a powerful debugger supporting the creation of new classes of mathematical objects and the installation of methods for computing specifically with them. Macaulay2 can compute Betti numbers, Ext, cohomology of coherent sheaves on projective varieties, primary decomposition of ideals, integral closure of rings, and more. Computer algebra system (CAS).

This software is also referenced in ORMS.


References in zbMATH (referenced in 1611 articles , 2 standard articles )

Showing results 21 to 40 of 1611.
Sorted by year (citations)

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  1. Böhm, Janko; Papadakis, Stavros Argyrios: Weak Lefschetz property and stellar subdivisions of Gorenstein complexes (2020)
  2. Boij, Mats; Teitler, Zach: A bound for the Waring rank of the determinant via syzygies (2020)
  3. Bolognesi, Michele; Pedrini, Claudio: The transcendental motive of a cubic fourfold (2020)
  4. Bolognini, Davide; Fugacci, Ulderico: Betti splitting from a topological point of view (2020)
  5. Botbol, Nicolás; Busé, Laurent; Chardin, Marc; Yildirim, Fatmanur: Fibers of multi-graded rational maps and orthogonal projection onto rational surfaces (2020)
  6. Bourget, Antoine; Cabrera, Santiago; Grimminger, Julius F.; Hanany, Amihay; Zhong, Zhenghao: Brane webs and magnetic quivers for SQCD (2020)
  7. Boyana Martinova, Marcus Robinson, Karl Schwede, Yuhui Yao: FastLinAlg package for Macaulay2 (2020) arXiv
  8. Brown, Gavin; Fatighenti, Enrico: Hodge numbers and deformations of Fano 3-folds (2020)
  9. Burity, Ricardo; Miranda-Neto, Cleto B.: The module of logarithmic derivations of a generic determinantal ideal (2020)
  10. Casella, Alex; Katerba, Charles; Tillmann, Stephan: Ideal points of character varieties, algebraic non-integral representations, and undetected closed essential surfaces in 3-manifolds (2020)
  11. Catalisano, Maria Virginia; Guardo, Elena; Shin, Yong-Su: The Waldschmidt constant of special (\Bbbk)-configurations in (\mathbbP^n) (2020)
  12. Celikbas, Ela; Laxmi, Jai; Kraśkiewicz, Witold; Weyman, Jerzy: The family of perfect ideals of codimension 3, of type 2 with 5 generators (2020)
  13. Chen, Justin; Dey, Papri: Computing symmetric determinantal representations (2020)
  14. Chen, Justin; Eur, Christopher; Yang, Greg; Zhang, Mengyuan: Free resolutions of function classes via order complexes (2020)
  15. Cid-Ruiz, Yairon: Multiplicity of the saturated special fiber ring of height two perfect ideals (2020)
  16. Cid-Ruiz, Yairon; Jafari, Sepehr; Nemati, Navid; Picone, Beatrice: Regularity of bicyclic graphs and their powers (2020)
  17. Cifuentes, Diego; Kahle, Thomas; Parrilo, Pablo: Sums of squares in Macaulay2 (2020)
  18. Ciupercă, Cătălin: Derivations and rational powers of ideals (2020)
  19. Clarke, Oliver; Mohammadi, Fatemeh: Toric degenerations of Grassmannians and Schubert varieties from matching field tableaux (2020)
  20. Cluzeau, Thomas; Koutschan, Christoph; Quadrat, Alban; Tõnso, Maris: Effective algebraic analysis approach to linear systems over Ore algebras (2020)

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Further publications can be found at: http://www.math.uiuc.edu/Macaulay2/Publications/