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 1579 articles , 2 standard articles )

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  1. Abbott, John; Bigatti, Anna Maria; Palezzato, Elisa; Robbiano, Lorenzo: Computing and using minimal polynomials (2020)
  2. Alfaro, Carlos A.: On graphs with 2 trivial distance ideals (2020)
  3. Alfaro, Carlos A.; Taylor, Libby: Distance ideals of graphs (2020)
  4. Altafi, Nasrin; Boij, Mats: The weak Lefschetz property of equigenerated monomial ideals (2020)
  5. Altafi, Nasrin; Nemati, Navid: Lefschetz properties of monomial algebras with almost linear resolution (2020)
  6. Amata, Luca; Crupi, Marilena: Hilbert functions of graded modules over an exterior algebra: an algorithmic approach (2020)
  7. Ananthnarayan, H.; Kumar, Rajiv: Extremal rays of Betti cones (2020)
  8. Andrade, Aline V.; Marchesi, Simone; Miró-Roig, Rosa M.: Irreducibility of the moduli space of orthogonal instanton bundles on (\mathbbP^n) (2020)
  9. Angelini, Elena; Chiantini, Luca: On the identifiability of ternary forms (2020)
  10. Antonio Macchia, Amy Wiebe: Slack Ideals in Macaulay2 (2020) arXiv
  11. Ballico, Edoardo; Ventura, Emanuele: Labels of real projective varieties (2020)
  12. Berget, Andrew: A type B analog of the Lie representation (2020)
  13. Berkesch, Christine; Matusevich, Laura Felicia; Walther, Uli: On normalized Horn systems (2020)
  14. Bernstein, Daniel Irving; Blekherman, Grigoriy; Sinn, Rainer: Typical and generic ranks in matrix completion (2020)
  15. Bernstein, Daniel Irving; Farnsworth, Cameron; Rodriguez, Jose Israel: The algebraic matroid of the finite unit norm tight frame (funtf) variety (2020)
  16. Bisui, Sankhaneel; Hà, Huy Tài; Thomas, Abu Chackalamannil: Fiber invariants of projective morphisms and regularity of powers of ideals (2020)
  17. Böhm, Janko; Papadakis, Stavros Argyrios: Weak Lefschetz property and stellar subdivisions of Gorenstein complexes (2020)
  18. Boij, Mats; Teitler, Zach: A bound for the Waring rank of the determinant via syzygies (2020)
  19. Bolognesi, Michele; Pedrini, Claudio: The transcendental motive of a cubic fourfold (2020)
  20. Bourget, Antoine; Cabrera, Santiago; Grimminger, Julius F.; Hanany, Amihay; Zhong, Zhenghao: Brane webs and magnetic quivers for SQCD (2020)

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