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 1364 articles , 2 standard articles )

Showing results 1 to 20 of 1364.
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  1. Colarte, Liena; Miró-Roig, Rosa M.: Minimal set of binomial generators for certain Veronese 3-fold projections (2020)
  2. Harris, Corey; Helmer, Martin: Segre class computation and practical applications (2020)
  3. Alberto F. Boix, Daniel J. Hernández, Zhibek Kadyrsizova, Mordechai Katzman, Sara Malec, Marcus Robinson, Karl Schwede, Daniel Smolkin, Pedro Teixeira, Emily E. Witt: The TestIdeals package for Macaulay2 (2019) arXiv
  4. Almeida, Charles; Andrade, Aline V.; Miró-Roig, Rosa M.: Gaps in the number of generators of monomial Togliatti systems (2019)
  5. Amata, Luca; Crupi, Marilena: Computation of graded ideals with given extremal Betti numbers in a polynomial ring (2019)
  6. 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)
  7. Ananthnarayan, H.; Celikbas, Ela; Laxmi, Jai; Yang, Zheng: Decomposing Gorenstein rings as connected sums (2019)
  8. Angelini, Elena: Waring decompositions and identifiability via Bertini and Macaulay2 software (2019)
  9. Aoki, Satoshi: Characterizations of indicator functions and contrast representations of fractional factorial designs with multi-level factors (2019)
  10. Ayah Almousa, Juliette Bruce, Michael C. Loper, Mahrud Sayrafi: The Virtual Resolutions Package for Macaulay2 (2019) arXiv
  11. 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)
  12. Barrera, Roberto: Computing quasidegrees of A-graded modules (2019)
  13. Bitoun, Thomas; Bogner, Christian; Klausen, René Pascal; Panzer, Erik: Feynman integral relations from parametric annihilators (2019)
  14. Bolognesi, Michele; Russo, Francesco; Staglianò, Giovanni: Some loci of rational cubic fourfolds (2019)
  15. Brenner, Holger; Caminata, Alessio: Differential symmetric signature in high dimension (2019)
  16. Cabrera, Santiago; Hanany, Amihay; Kalveks, Rudolph: Quiver theories and formulae for Slodowy slices of classical algebras (2019)
  17. Chan, Andrew J.; Maclagan, Diane: Gröbner bases over fields with valuations (2019)
  18. Chen, Justin: Matroids: a Macaulay2 package (2019)
  19. Chen, Justin; Kileel, Joe: Numerical implicitization: a Macaulay2 package (2019)
  20. C.J. Bott, S. Hamid Hassanzadeh, Karl Schwede, Daniel Smolkin: RationalMaps, a package for Macaulay2 (2019) arXiv

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