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 1321 to 1340 of 1438.
Sorted by year (citations)

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  1. Smith, Gregory G.: Teaching the geometry of schemes (2002)
  2. Sottile, Frank: From enumerative geometry to solving systems of polynomial equations (2002)
  3. Stillman, Michael; Sturmfels, Bernd; Thomas, Rekha: Algorithms for the toric Hilbert scheme (2002)
  4. Sturmfels, Bernd: Ideals, varieties and Macaulay 2 (2002)
  5. Suciu, Alexander I.: Translated tori in the characteristic varieties of complex hyperplane arrangements (2002)
  6. Theobald, Thorsten: Computing amoebas (2002)
  7. Tsai, Harrison: Algorithms for associated primes, Weyl closure, and local cohomology of (D)-modules (2002)
  8. Walther, Uli: (D)-modules and cohomology of varieties (2002)
  9. Blum, Stefan: Base-sortable matroids and Koszulness of semigroup rings (2001)
  10. Brodmann, Markus; Schenzel, Peter: Curves of degree (r+2) in (\mathbbP^r): Cohomological, geometric, and homological aspects (2001)
  11. Buchberger, Bruno: Gröbner bases: A short introduction for systems theorists (2001)
  12. Ciupercă, Cătălin: First coefficient ideals and the (S_2)-ification of a Rees algebra (2001)
  13. Decker, W.; Schreyer, F.-O.: Computational algebraic geometry today (2001)
  14. Haiman, Mark: Hilbert schemes, polygraphs and the Macdonald positivity conjecture (2001)
  15. Iliev, Atanas; Ranestad, Kristian: (K3) surfaces of genus 8 and varieties of sums of powers of cubic fourfolds (2001)
  16. Johnson, Mark R.; Morey, Susan: Normal blow-ups and their expected defining equations (2001)
  17. Li, Qiang; Guo, Yi-ke; Darlington, John; Ida, Tetsuo: Minimised geometric Buchberger algorithm for integer programming (2001)
  18. Maekawa, Masahide; Noro, Masayuki; Takayama, Nobuki; Tamura, Yasushi; Ohara, Katsuyoshi: The design and implementation of OpenXM-RFC 100 and 101 (2001)
  19. Oaku, Toshinori; Takayama, Nobuki; Tsai, Harrison: Polynomial and rational solutions of holonomic systems (2001)
  20. Schreyer, Frank-Olaf: Geometry and algebra of prime Fano 3-folds of genus 12. (2001)

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