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 1306 articles , 2 standard articles )

Showing results 1 to 20 of 1306.
Sorted by year (citations)

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  1. 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)
  2. Almeida, Charles; Andrade, Aline V.; Miró-Roig, Rosa M.: Gaps in the number of generators of monomial Togliatti systems (2019)
  3. Angelini, Elena: Waring decompositions and identifiability via Bertini and Macaulay2 software (2019)
  4. Chan, Andrew J.; Maclagan, Diane: Gröbner bases over fields with valuations (2019)
  5. 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)
  6. Cueto, Maria Angelica; Markwig, Hannah: Tropical geometry of genus two curves (2019)
  7. Cunha, Rainelly; Ramos, Zaqueu; Simis, Aron: Symmetry preserving degenerations of the generic symmetric matrix (2019)
  8. Dao, Hailong; Montaño, Jonathan: Length of local cohomology of powers of ideals (2019)
  9. De Loera, Jesús A.; Petrović, Sonja; Silverstein, Lily; Stasi, Despina; Wilburne, Dane: Random monomial ideals (2019)
  10. Dipasquale, Michael; Francisco, Christopher A.; Mermin, Jeffrey; Schweig, Jay; Sosa, Gabriel: The Rees algebra of a two-Borel ideal is Koszul (2019)
  11. Erman, Daniel; Sam, Steven V.; Snowden, Andrew: Cubics in 10 variables vs. cubics in 1000 variables: uniformity phenomena for bounded degree polynomials (2019)
  12. Faenzi, Daniele; Polizzi, Francesco; Vallès, Jean: Triple planes with $p_g=q=0$ (2019)
  13. Lundqvist, Samuel; Nicklasson, Lisa: On the structure of monomial complete intersections in positive characteristic (2019)
  14. Lundqvist, Samuel; Oneto, Alessandro; Reznick, Bruce; Shapiro, Boris: On generic and maximal $k$-ranks of binary forms (2019)
  15. Manjunath, Madhusudan; Smith, Ben: Commutative algebra of generalised Frobenius numbers (2019)
  16. Mayes-Tang, Sarah: Stabilization of Boij-Söderberg decompositions of ideal powers (2019)
  17. Michael Lesnick, Matthew Wright: Computing Minimal Presentations and Betti Numbers of 2-Parameter Persistent Homology (2019) arXiv
  18. Rather, Shahnawaz Ahmad; Singh, Pavinder: On Betti numbers of edge ideals of crown graphs (2019)
  19. Steiner, Avi: $A$-hypergeometric modules and Gauss-Manin systems (2019)
  20. Trung, Van Duc: The initial ideal of generic sequences and Fröberg’s conjecture (2019)

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