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 1567 articles , 2 standard articles )

Showing results 41 to 60 of 1567.
Sorted by year (citations)

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  1. Di Rocco, Sandra; Eklund, David; Weinstein, Madeleine: The bottleneck degree of algebraic varieties (2020)
  2. Duarte, Eliana; Görgen, Christiane: Equations defining probability tree models (2020)
  3. Gouveia, João; Macchia, Antonio; Thomas, Rekha R.; Wiebe, Amy: Projectively unique polytopes and toric slack ideals (2020)
  4. Hà, Huy Tài; Nguyen, Hop Dang; Trung, Ngo Viet; Trung, Tran Nam: Symbolic powers of sums of ideals (2020)
  5. Harris, Corey; Helmer, Martin: Segre class computation and practical applications (2020)
  6. Iarrobino, Anthony; Macias Marques, Pedro; McDaniel, Chris: Free extensions and Jordan type (2020)
  7. Iohara, Kenji (ed.); Malbos, Philippe (ed.); Saito, Masa-Hiko (ed.); Takayama, Nobuki (ed.): Two algebraic byways from differential equations: Gröbner bases and quivers (2020)
  8. Jafarloo, Iman Bahmani; Carlini, Enrico: Special apolar subset: the case of star configurations (2020)
  9. Kim, Yeongrak; Schreyer, Frank-Olaf: An explicit matrix factorization of cubic hypersurfaces of small dimension (2020)
  10. Koutsoumpelias, Alexandros Grosdos; Wageringel, Markus: Moment ideals of local Dirac mixtures (2020)
  11. Kumar, Arvind: Regularity bound of generalized binomial edge ideal of graphs (2020)
  12. Mandal, Mousumi; Nanduri, Ramakrishna: Regularity comparison of fiber cone and associated graded ring (2020)
  13. Martínez-Bernal, José; Valencia-Bucio, Miguel A.; Villarreal, Rafael H.: Linear codes over signed graphs (2020)
  14. Menini, Laura; Possieri, Corrado; Tornambè, Antonio: A symbolic algorithm to compute immersions of polynomial systems into linear ones up to an output injection (2020)
  15. Miró-Roig, Rosa M.; Tran, Quang Hoa: On the weak Lefschetz property for almost complete intersections generated by uniform powers of general linear forms (2020)
  16. Mohammadi, Fatemeh; Pascual-Ortigosa, Patricia; Sáenz-de-Cabezón, Eduardo; Wynn, Henry P.: Polarization and depolarization of monomial ideals with application to multi-state system reliability (2020)
  17. Rennemo, Jørgen Vold: The homological projective dual of (\operatornameSym^2\mathbbP(V)) (2020)
  18. Sammartano, Alessio: Blowup algebras of rational normal scrolls (2020)
  19. Saremi, Hero; Mafi, Amir: Unmixedness and arithmetic properties of matroidal ideals (2020)
  20. Sarkar, Parangama: Rees’ theorem for filtrations, multiplicity function and reduction criteria (2020)

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