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 1501 to 1520 of 1567.
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  1. Vargas, J. A.; del Castillo, Rafael F.: Inbreeding depression in a zygotic algebra (1999)
  2. Abo, Hirotachi; Decker, Wolfram; Sasakura, Nobuo: An elliptic conic bundle in (\mathbbP^4) arising from a stable rank-3 vector bundle (1998)
  3. Brundu, M.; Logar, A.: Parametrization of the orbits of cubic surfaces (1998)
  4. Costa, Laura: An explicit description of some surfaces of degree 8 in (\mathbbP^5) (1998)
  5. De Jong, Theo: An algorithm for computing the integral closure (1998)
  6. Green, Marc; Stillman, Michael: A tutorial on generic initial ideals (1998)
  7. Greuel, Gert-Martin; Pfister, Gerhard: Gröbner bases and algebraic geometry (1998)
  8. Greuel, G. M.: Standard bases and applications (1998)
  9. Haiman, Mark: (t,q)-Catalan numbers and the Hilbert scheme. (1998)
  10. La Scala, Roberto; Stillman, Michael: Strategies for computing minimal free resolutions (1998)
  11. Ottaviani, Giorgio: Real and complex ’t Hooft instanton bundles over (\mathbbP^2n+1(\mathbbC)). -- Appendix (1998)
  12. Peterson, Christopher S.: Quasi complete intersections, powers of ideals and deficiency modules (1998)
  13. Reeves, Alyson A.: A parallel implementation of Buchberger’s algorithm over (\mathbbZ_p) for (p\leq31991) (1998)
  14. Shin, Yong Su: The construction of some Gorenstein ideals of codimension (4) (1998)
  15. Vasconcelos, Wolmer V.: Computational methods of commutative algebra and algebraic geometry. With chapters by David Eisenbud, Daniel R. Grayson, Jürgen Herzog and Michael Stillman (1998)
  16. Vasconcelos, Wolmer V.: The homological degree of a module (1998)
  17. Aure, Alf; Decker, Wolfram; Hulek, Klaus; Popescu, Sorin; Ranestad, Kristian: Syzygies of abelian and bielliptic surfaces in (\mathbbP^4). -- Appendix by C. Ciliberto and K. Hulek (1997)
  18. Boffi, G.; Bruns, W.; Guerrieri, A.: On the Jacobian ideal of a trilinear form (1997)
  19. Capani, A.; De Dominicis, G.; Niesi, G.; Robbiano, L.: Computing minimal finite free resolutions (1997)
  20. Corso, Alberto; Polini, Claudia: Reduction number of links of irreducible varieties (1997)

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