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 41 to 60 of 1611.
Sorted by year (citations)

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  1. Colarte, Liena; Miró-Roig, Rosa M.: Minimal set of binomial generators for certain Veronese 3-fold projections (2020)
  2. Conca, Aldo; Varbaro, Matteo: Square-free Gröbner degenerations (2020)
  3. 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)
  4. Cortadellas Benítez, Teresa; Cox, David A.; D’Andrea, Carlos: The Rees algebra of parametric curves via liftings (2020)
  5. Cortadellas Benítez, Teresa; D’Andrea, Carlos; Enescu, Florian: On the resolution of fan algebras of principal ideals over a Noetherian ring (2020)
  6. Croll, Amanda; Dellaca, Roger; Gupta, Anjan; Hoffmeier, Justin; Mukundan, Vivek; Şega, Liana M.; Sosa, Gabriel; Thompson, Peder; Rangel Tracy, Denise: Detecting Koszulness and related homological properties from the algebra structure of Koszul homology (2020)
  7. Cường, Đoàn Trung; Kwak, Sijong: The reduction number and degree bound of projective subschemes (2020)
  8. Dao, Hailong; Montaño, Jonathan: On asymptotic vanishing behavior of local cohomology (2020)
  9. Debarre, Olivier; Han, Frédéric; O’Grady, Kieran; Voisin, Claire: Hilbert squares of (K3) surfaces and Debarre-Voisin varieties (2020)
  10. Dey, Papri; Görlach, Paul; Kaihnsa, Nidhi: Coordinate-wise powers of algebraic varieties (2020)
  11. Dey, Papri; Plaumann, Daniel: Testing hyperbolicity of real polynomials (2020)
  12. Di Marca, Michela; Malara, Grzegorz; Oneto, Alessandro: Unexpected curves arising from special line arrangements (2020)
  13. DiPasquale, Michael; Francisco, Christopher A.; Mermin, Jeffrey; Schweig, Jay: Free and non-free multiplicities on the (A_3) arrangement (2020)
  14. DiPasquale, Michael; Sottile, Frank: Bivariate semialgebraic splines (2020)
  15. Di Rocco, Sandra; Eklund, David; Weinstein, Madeleine: The bottleneck degree of algebraic varieties (2020)
  16. Duarte, Eliana; Görgen, Christiane: Equations defining probability tree models (2020)
  17. Duarte, Eliana; Seceleanu, Alexandra: Implicitization of tensor product surfaces via virtual projective resolutions (2020)
  18. Favacchio, Giuseppe; Keiper, Graham; van Tuyl, Adam: Regularity and (h)-polynomials of toric ideals of graphs (2020)
  19. Fouli, Louiza; Hà, Huy Tài; Morey, Susan: Initially regular sequences and depths of ideals (2020)
  20. Fouli, Louiza; Hà, Huy Tài; Morey, Susan: Depth of powers of squarefree monomial ideals (research) (2020)

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