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 1579 articles , 2 standard articles )

Showing results 1501 to 1520 of 1579.
Sorted by year (citations)

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  1. Peeva, Irena; Stillman, Mike: Local equations for the toric Hilbert scheme (2000)
  2. Ranestad, Kristian; Schreyer, Frank-Olaf: Varieties of sums of powers (2000)
  3. Smith, Gregory G.: Computing global extension modules (2000)
  4. Sturmfels, Bernd: Four counterexamples in combinatorial algebraic geometry (2000)
  5. Vargas, J. A.: Hardy-Weinberg theory for tetraploidy with mixed mating (2000)
  6. Bayer, Dave; Charalambous, Hara; Popescu, Sorin: Extremal Betti numbers and applications to monomial ideals (1999)
  7. Bernasconi, Anna; Egidi, Lavinia: Hilbert function and complexity lower bounds for symmetric Boolean functions (1999)
  8. Boij, Mats: Gorenstein algebras with nonunimodal Betti numbers (1999)
  9. Holland, Martin P.; Mond, David: Stable mappings and logarithmic relative symplectic forms (1999)
  10. Katzman, Mordechai: Bipartite graphs whose edge algebras are complete intersections (1999)
  11. Matsumoto, Ryutaroh; Miura, Shinji: Computing a basis of (\mathfrakL (D)) on an affine algebraic curve with one rational place at infinity (1999)
  12. Stillman, Michael; Tsai, Harrison: Using SAGBI bases to compute invariants (1999)
  13. Vargas, J. A.; del Castillo, Rafael F.: Inbreeding depression in a zygotic algebra (1999)
  14. Abo, Hirotachi; Decker, Wolfram; Sasakura, Nobuo: An elliptic conic bundle in (\mathbbP^4) arising from a stable rank-3 vector bundle (1998)
  15. Brundu, M.; Logar, A.: Parametrization of the orbits of cubic surfaces (1998)
  16. Costa, Laura: An explicit description of some surfaces of degree 8 in (\mathbbP^5) (1998)
  17. De Jong, Theo: An algorithm for computing the integral closure (1998)
  18. Green, Marc; Stillman, Michael: A tutorial on generic initial ideals (1998)
  19. Greuel, Gert-Martin; Pfister, Gerhard: Gröbner bases and algebraic geometry (1998)
  20. Greuel, G. M.: Standard bases and applications (1998)

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