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 1658 articles , 2 standard articles )

Showing results 1 to 20 of 1658.
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  1. Brysiewicz, Taylor: Necklaces count polynomial parametric osculants (2021)
  2. Cid-Ruiz, Yairon: Mixed multiplicities and projective degrees of rational maps (2021)
  3. Dochtermann, Anton: Exposed circuits, linear quotients, and chordal clutters (2021)
  4. Duarte, Eliana; Marigliano, Orlando; Sturmfels, Bernd: Discrete statistical models with rational maximum likelihood estimator (2021)
  5. Gao, Jiyang; Li, Yutong; Loper, Michael C.; Mattoo, Amal: Virtual complete intersections in (\mathbbP^1\times\mathbbP^1) (2021)
  6. Iarrobino, Anthony; Macias Marques, Pedro: Symmetric decomposition of the associated graded algebra of an Artinian Gorenstein algebra (2021)
  7. Jaramillo, Delio; Villarreal, Rafael H.: The (v)-number of edge ideals (2021)
  8. Kinser, Ryan; Rajchgot, Jenna: Type (D) quiver representation varieties, double Grassmannians, and symmetric varieties (2021)
  9. Kohn, Kathlén: Coisotropic hypersurfaces in Grassmannians (2021)
  10. Mantero, Paolo; Mastroeni, Matthew: Betti numbers of Koszul algebras defined by four quadrics (2021)
  11. Raicu, Claudiu: Regularity of (\mathfrakS_n)-invariant monomial ideals (2021)
  12. Abbott, John; Bigatti, Anna Maria; Palezzato, Elisa; Robbiano, Lorenzo: Computing and using minimal polynomials (2020)
  13. Adamer, Michael F.; Helmer, Martin: Families of toric chemical reaction networks (2020)
  14. Alfaro, Carlos A.: On graphs with 2 trivial distance ideals (2020)
  15. Alfaro, Carlos A.; Taylor, Libby: Distance ideals of graphs (2020)
  16. Altafi, Nasrin; Boij, Mats: The weak Lefschetz property of equigenerated monomial ideals (2020)
  17. Altafi, Nasrin; Nemati, Navid: Lefschetz properties of monomial algebras with almost linear resolution (2020)
  18. Amata, Luca; Crupi, Marilena: Hilbert functions of graded modules over an exterior algebra: an algorithmic approach (2020)
  19. Ananthnarayan, H.; Kumar, Rajiv: Extremal rays of Betti cones (2020)
  20. Andrade, Aline V.; Marchesi, Simone; Miró-Roig, Rosa M.: Irreducibility of the moduli space of orthogonal instanton bundles on (\mathbbP^n) (2020)

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