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 1438 articles , 2 standard articles )

Showing results 21 to 40 of 1438.
Sorted by year (citations)

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  1. Aoki, Satoshi: Characterizations of indicator functions and contrast representations of fractional factorial designs with multi-level factors (2019)
  2. Ayah Almousa, Juliette Bruce, Michael C. Loper, Mahrud Sayrafi: The Virtual Resolutions Package for Macaulay2 (2019) arXiv
  3. Banerjee, Arindam; Mukundan, Vivek: The powers of unmixed bipartite edge ideals (2019)
  4. Baños, Hector; Bushek, Nathaniel; Davidson, Ruth; Gross, Elizabeth; Harris, Pamela E.; Krone, Robert; Long, Colby; Stewart, Allen; Walker, Robert: Dimensions of group-based phylogenetic mixtures (2019)
  5. Barrera, Roberto: Computing quasidegrees of A-graded modules (2019)
  6. Berkesch, Christine; Matusevich, Laura Felicia; Walther, Uli: Torus equivariant (D)-modules and hypergeometric systems (2019)
  7. Bitoun, Thomas; Bogner, Christian; Klausen, René Pascal; Panzer, Erik: Feynman integral relations from parametric annihilators (2019)
  8. Boege, Tobias; D’Alì, Alessio; Kahle, Thomas; Sturmfels, Bernd: The geometry of gaussoids (2019)
  9. Boix, Alberto F.; Zarzuela, Santiago: Frobenius and Cartier algebras of Stanley-Reisner rings. II (2019)
  10. Bolognesi, Michele; Russo, Francesco; Staglianò, Giovanni: Some loci of rational cubic fourfolds (2019)
  11. Bouchat, Rachelle R.; Brown, Tricia Muldoon: Fibonacci numbers and resolutions of domino ideals (2019)
  12. Brandt, Madeline; Wiebe, Amy: The slack realization space of a matroid (2019)
  13. Brenner, Holger; Caminata, Alessio: Differential symmetric signature in high dimension (2019)
  14. Cabrera, Santiago; Hanany, Amihay; Kalveks, Rudolph: Quiver theories and formulae for Slodowy slices of classical algebras (2019)
  15. Catalisano, M. V.; Geramita, A. V.; Gimigliano, A.; Harbourne, B.; Migliore, J.; Nagel, U.; Shin, Y. S.: Secant varieties of the varieties of reducible hypersurfaces in (\mathbbP^n) (2019)
  16. Chan, Andrew J.; Maclagan, Diane: Gröbner bases over fields with valuations (2019)
  17. Chardin, Marc; Naéliton, José; Tran, Quang Hoa: Cohen-Macaulayness and canonical module of residual intersections (2019)
  18. Chen, Justin: Matroids: a Macaulay2 package (2019)
  19. Chen, Justin; Kileel, Joe: Numerical implicitization: a Macaulay2 package (2019)
  20. Christandl, Matthias; Gesmundo, Fulvio; Jensen, Asger Kjærulff: Border rank is not multiplicative under the tensor product (2019)

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