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 910 articles , 2 standard articles )

Showing results 1 to 20 of 910.
Sorted by year (citations)

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  1. Prabhu-Naik, Nathan: Tilting bundles on toric Fano fourfolds (2017)
  2. Abo, Hirotachi; Eklund, David; Kahle, Thomas; Peterson, Chris: Eigenschemes and the Jordan canonical form (2016)
  3. Alberich-Carramiñana, Maria; Dachs-Cadefau, Ferran; Àlvarez Montaner, Josep: Multiplier ideals in two-dimensional local rings with rational singularities (2016)
  4. Anzis, Benjamin; Tohǎneanu, Ştefan O.: On the geometry of real or complex supersolvable line arrangements (2016)
  5. Ballico, Edoardo; Dumitrescu, Olivia; Postinghel, Elisa: On Segre’s bound for fat points in $\mathbbP^n$ (2016)
  6. Barile, Margherita; Macchia, Antonio: The arithmetical rank of the edge ideals of graphs with pairwise disjoint cycles (2016)
  7. Bocci, Cristiano; Carlini, Enrico; Kileel, Joe: Hadamard products of linear spaces (2016)
  8. Boels, Rutger H.; Kniehl, Bernd A.; Yang, Gang: Master integrals for the four-loop Sudakov form factor (2016)
  9. Boggess, Brandon: Splitting varieties for cup products with $\mathbbZ/3$-coefficients (2016)
  10. Böhm, Janko; Decker, Wolfram; Keicher, Simon; Ren, Yue: Current challenges in developing open source computer algebra systems (2016)
  11. Bolognesi, Michele; Massarenti, Alex: Moduli of abelian surfaces, symmetric theta structures and theta characteristics (2016)
  12. Bolognini, Davide: Recursive Betti numbers for Cohen-Macaulay $d$-partite clutters arising from posets (2016)
  13. Bolognini, Davide: Betti splitting via componentwise linear ideals (2016)
  14. Boocher, Adam; D’Alì, Alessio; Grifo, Eloísa; Montaño, Jonathan; Sammartano, Alessio: On the growth of deviations (2016)
  15. Botbol, Nicolás; Dickenstein, Alicia: Implicitization of rational hypersurfaces via linear syzygies: a practical overview (2016)
  16. Brambilla, Maria Chiara; Dumitrescu, Olivia; Postinghel, Elisa: On linear systems of $\mathbb P^3$ with nine base points (2016)
  17. Cassidy, Thomas; Conner, Andrew; Kirkman, Ellen; Moore, W.Frank: Periodic free resolutions from twisted matrix factorizations (2016)
  18. Caviglia, Giulio; Sbarra, Enrico: The lex-plus-powers inequality for local cohomology modules (2016)
  19. Chipalkatti, Jaydeep: On the coincidences of Pascal lines (2016)
  20. Crupi, Marilena: Extremal Betti numbers of graded modules (2016)

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