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 1538 articles , 2 standard articles )

Showing results 1 to 20 of 1538.
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  1. Abbott, John; Bigatti, Anna Maria; Palezzato, Elisa; Robbiano, Lorenzo: Computing and using minimal polynomials (2020)
  2. Alfaro, Carlos A.; Taylor, Libby: Distance ideals of graphs (2020)
  3. Altafi, Nasrin; Nemati, Navid: Lefschetz properties of monomial algebras with almost linear resolution (2020)
  4. Amata, Luca; Crupi, Marilena: Hilbert functions of graded modules over an exterior algebra: an algorithmic approach (2020)
  5. Andrade, Aline V.; Marchesi, Simone; Miró-Roig, Rosa M.: Irreducibility of the moduli space of orthogonal instanton bundles on (\mathbbP^n) (2020)
  6. Bernstein, Daniel Irving; Blekherman, Grigoriy; Sinn, Rainer: Typical and generic ranks in matrix completion (2020)
  7. Bernstein, Daniel Irving; Farnsworth, Cameron; Rodriguez, Jose Israel: The algebraic matroid of the finite unit norm tight frame (funtf) variety (2020)
  8. Bolognesi, Michele; Pedrini, Claudio: The transcendental motive of a cubic fourfold (2020)
  9. Boyana Martinova, Marcus Robinson, Karl Schwede, Yuhui Yao: FastLinAlg package for Macaulay2 (2020) arXiv
  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. Cid-Ruiz, Yairon: Multiplicity of the saturated special fiber ring of height two perfect ideals (2020)
  12. Ciupercă, Cătălin: Derivations and rational powers of ideals (2020)
  13. Colarte, Liena; Miró-Roig, Rosa M.: Minimal set of binomial generators for certain Veronese 3-fold projections (2020)
  14. Cooper, Susan M.; Seceleanu, Alexandra; Tohăneanu, Ştefan O.; Vaz Pinto, Maria; Villarreal, Rafael H.: Generalized minimum distance functions and algebraic invariants of Geramita ideals (2020)
  15. Cortadellas Benítez, Teresa; Cox, David A.; D’Andrea, Carlos: The Rees algebra of parametric curves via liftings (2020)
  16. Cortadellas Benítez, Teresa; D’Andrea, Carlos; Enescu, Florian: On the resolution of fan algebras of principal ideals over a Noetherian ring (2020)
  17. Cường, Đoàn Trung; Kwak, Sijong: The reduction number and degree bound of projective subschemes (2020)
  18. Di Marca, Michela; Malara, Grzegorz; Oneto, Alessandro: Unexpected curves arising from special line arrangements (2020)
  19. DiPasquale, Michael; Francisco, Christopher A.; Mermin, Jeffrey; Schweig, Jay: Free and non-free multiplicities on the (A_3) arrangement (2020)
  20. DiPasquale, Michael; Sottile, Frank: Bivariate semialgebraic splines (2020)

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