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 1485 articles , 2 standard articles )

Showing results 1301 to 1320 of 1485.
Sorted by year (citations)

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  1. Vinai, Natale Paolo: Arithmetic degree and associated graded modules (2004)
  2. Wijnholt, Martijn: Large volume perspective on branes at singularities (2004)
  3. Aluffi, Paolo: Computing characteristic classes of projective schemes. (2003)
  4. Arnold, Elizabeth A.: Modular algorithms for computing Gröbner bases. (2003)
  5. Baines, Rosemary; Vámos, Peter: An algorithm to compute the set of characteristics of a system of polynomial equations over the integers. (2003)
  6. Behrend, K.; O’Halloran, A.: On the cohomology of stable map spaces (2003)
  7. Castro-Jiménez, Francisco Jesús; Takayama, Nobuki: Singularities of the hypergeometric system associated with a monomial curve (2003)
  8. Ciupercă, Cătălin: A numerical characterization of the (S_2)-ification of a Rees algebra (2003)
  9. Cox, David: Curves, surfaces, and syzygies (2003)
  10. Datta, Ruchira S.: Using computer algebra to find Nash equilibria (2003)
  11. De Loera, Jesús A.; Sturmfels, Bernd: Algebraic unimodular counting (2003)
  12. Dumas, Jean-Guillaume; Heckenbach, Frank; Saunders, David; Welker, Volkmar: Computing simplicial homology based on efficient Smith normal form algorithms (2003)
  13. Eisenbud, David; Fløystad, Gunnar; Schreyer, Frank-Olaf: Sheaf cohomology and free resolutions over exterior algebras (2003)
  14. Eisenbud, David; Hulek, Klaus; Popescu, Sorin: A note on the intersection of Veronese surfaces (2003)
  15. Eisenbud, David; Popescu, Sorin; Yuzvinsky, Sergey: Hyperplane arrangement cohomology and monomials in the exterior algebra (2003)
  16. Eisenbud, David; Weyman, Jerzy: Fitting’s lemma for (\mathbbZ/2)-graded modules (2003)
  17. Endrass, Stephan; Persson, Ulf; Stevens, Jan: Surfaces with triple points. (2003)
  18. Francisco, Christopher A.: Minimal graded Betti numbers and stable ideals (2003)
  19. Gago-Vargas, Jesús: Bases for projective modules in (A_n(k)). (2003)
  20. Gatermann, Karin: Applications of SAGBI-bases in dynamics (2003)

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