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 1326 articles , 2 standard articles )

Showing results 1 to 20 of 1326.
Sorted by year (citations)

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  1. Amata, Luca; Crupi, Marilena: Computation of graded ideals with given extremal Betti numbers in a polynomial ring (2019-2019)
  2. Améndola, Carlos; Bliss, Nathan; Burke, Isaac; Gibbons, Courtney R.; Helmer, Martin; Hoşten, Serkan; Nash, Evan D.; Rodriguez, Jose Israel; Smolkin, Daniel: The maximum likelihood degree of toric varieties (2019-2019)
  3. Almeida, Charles; Andrade, Aline V.; Miró-Roig, Rosa M.: Gaps in the number of generators of monomial Togliatti systems (2019)
  4. Ananthnarayan, H.; Celikbas, Ela; Laxmi, Jai; Yang, Zheng: Decomposing Gorenstein rings as connected sums (2019)
  5. Angelini, Elena: Waring decompositions and identifiability via Bertini and Macaulay2 software (2019)
  6. 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)
  7. Bitoun, Thomas; Bogner, Christian; Klausen, René Pascal; Panzer, Erik: Feynman integral relations from parametric annihilators (2019)
  8. Cabrera, Santiago; Hanany, Amihay; Kalveks, Rudolph: Quiver theories and formulae for Slodowy slices of classical algebras (2019)
  9. Chan, Andrew J.; Maclagan, Diane: Gröbner bases over fields with valuations (2019)
  10. Clark, Timothy B. P.; Tchernev, Alexandre B.: Minimal free resolutions of monomial ideals and of toric rings are supported on posets (2019)
  11. Colarte, Liena; Mezzetti, Emilia; Miró-Roig, Rosa M.; Salat, Martí: On the coefficients of the permanent and the determinant of a circulant matrix: applications (2019)
  12. Coskun, Izzet; Riedl, Eric: Normal bundles of rational curves on complete intersections (2019)
  13. Cueto, Maria Angelica; Markwig, Hannah: Tropical geometry of genus two curves (2019)
  14. Cunha, Rainelly; Ramos, Zaqueu; Simis, Aron: Symmetry preserving degenerations of the generic symmetric matrix (2019)
  15. Dao, Hailong; Montaño, Jonathan: Length of local cohomology of powers of ideals (2019)
  16. De Loera, Jesús A.; Petrović, Sonja; Silverstein, Lily; Stasi, Despina; Wilburne, Dane: Random monomial ideals (2019)
  17. DiPasquale, Michael; Francisco, Christopher A.; Mermin, Jeffrey; Schweig, Jay; Sosa, Gabriel: The Rees algebra of a two-Borel ideal is Koszul (2019)
  18. Erey, Nursel: Powers of ideals associated to ((C_4,2K_2))-free graphs (2019)
  19. Erman, Daniel; Sam, Steven V.; Snowden, Andrew: Cubics in 10 variables vs. cubics in 1000 variables: uniformity phenomena for bounded degree polynomials (2019)
  20. Faenzi, Daniele; Polizzi, Francesco; Vallès, Jean: Triple planes with (p_g=q=0) (2019)

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