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 41 to 60 of 1438.
Sorted by year (citations)

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  1. Chung, Kiryong; Yoo, Sang-Bum: Compactifications of conic spaces in Del Pezzo 3-fold (2019)
  2. C.J. Bott, S. Hamid Hassanzadeh, Karl Schwede, Daniel Smolkin: RationalMaps, a package for Macaulay2 (2019) arXiv
  3. Clark, Timothy B. P.; Tchernev, Alexandre B.: Minimal free resolutions of monomial ideals and of toric rings are supported on posets (2019)
  4. 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)
  5. Conca, Aldo; Nguyen, Hop D.; Vu, Thanh: Products of ideals of linear forms in quadric hypersurfaces (2019)
  6. Cook, David II: The uniform face ideals of a simplicial complex (2019)
  7. Coskun, Izzet; Riedl, Eric: Normal bundles of rational curves on complete intersections (2019)
  8. Crispin Quiñonez, Veronica; Lundqvist, Samuel; Nenashev, Gleb: On ideals generated by two generic quadratic forms in the exterior algebra (2019)
  9. Cueto, Maria Angelica; Markwig, Hannah: Tropical geometry of genus two curves (2019)
  10. Cunha, Rainelly; Ramos, Zaqueu; Simis, Aron: Symmetry preserving degenerations of the generic symmetric matrix (2019)
  11. D’Alì, Alessio; Fløystad, Gunnar; Nematbakhsh, Amin: Resolutions of co-letterplace ideals and generalizations of Bier spheres (2019)
  12. Daniel J. Hernández, Karl Schwede, Pedro Teixeira, Emily E. Witt: The FrobeniusThresholds package for Macaulay2 (2019) arXiv
  13. D’Anna, Marco; Jafari, Raheleh; Strazzanti, Francesco: Tangent cones of monomial curves obtained by numerical duplication (2019)
  14. Dao, Hailong; Montaño, Jonathan: Length of local cohomology of powers of ideals (2019)
  15. De Loera, Jesús A.; Hoşten, Serkan; Krone, Robert; Silverstein, Lily: Average behavior of minimal free resolutions of monomial ideals (2019)
  16. De Loera, Jesús A.; Petrović, Sonja; Silverstein, Lily; Stasi, Despina; Wilburne, Dane: Random monomial ideals (2019)
  17. De Negri, Emanuela; Sbarra, Enrico: On jet schemes of Pfaffian ideals (2019)
  18. DiPasquale, Michael; Francisco, Christopher A.; Mermin, Jeffrey; Schweig, Jay; Sosa, Gabriel: The Rees algebra of a two-Borel ideal is Koszul (2019)
  19. Donten-Bury, Maria; Grab, Maksymilian: Crepant resolutions of 3-dimensional quotient singularities via Cox rings (2019)
  20. Dubinsky, Manuel; Massri, César; Molinuevo, Ariel; Quallbrunn, Federico: DiffAlg: a differential algebra package (2019)

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