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 1567 articles , 2 standard articles )

Showing results 21 to 40 of 1567.
Sorted by year (citations)

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  1. Casella, Alex; Katerba, Charles; Tillmann, Stephan: Ideal points of character varieties, algebraic non-integral representations, and undetected closed essential surfaces in 3-manifolds (2020)
  2. Catalisano, Maria Virginia; Guardo, Elena; Shin, Yong-Su: The Waldschmidt constant of special (\Bbbk)-configurations in (\mathbbP^n) (2020)
  3. Celikbas, Ela; Laxmi, Jai; Kraśkiewicz, Witold; Weyman, Jerzy: The family of perfect ideals of codimension 3, of type 2 with 5 generators (2020)
  4. Chen, Justin; Dey, Papri: Computing symmetric determinantal representations (2020)
  5. Cid-Ruiz, Yairon: Multiplicity of the saturated special fiber ring of height two perfect ideals (2020)
  6. Cid-Ruiz, Yairon; Jafari, Sepehr; Nemati, Navid; Picone, Beatrice: Regularity of bicyclic graphs and their powers (2020)
  7. Cifuentes, Diego; Kahle, Thomas; Parrilo, Pablo: Sums of squares in Macaulay2 (2020)
  8. Ciupercă, Cătălin: Derivations and rational powers of ideals (2020)
  9. Colarte, Liena; Miró-Roig, Rosa M.: Minimal set of binomial generators for certain Veronese 3-fold projections (2020)
  10. 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)
  11. Cortadellas Benítez, Teresa; Cox, David A.; D’Andrea, Carlos: The Rees algebra of parametric curves via liftings (2020)
  12. Cortadellas Benítez, Teresa; D’Andrea, Carlos; Enescu, Florian: On the resolution of fan algebras of principal ideals over a Noetherian ring (2020)
  13. 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)
  14. Cường, Đoàn Trung; Kwak, Sijong: The reduction number and degree bound of projective subschemes (2020)
  15. Dao, Hailong; Montaño, Jonathan: On asymptotic vanishing behavior of local cohomology (2020)
  16. Debarre, Olivier; Han, Frédéric; O’Grady, Kieran; Voisin, Claire: Hilbert squares of K3 surfaces and Debarre-Voisin varieties (2020)
  17. Dey, Papri; Plaumann, Daniel: Testing hyperbolicity of real polynomials (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/