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 1353 articles , 2 standard articles )

Showing results 1301 to 1320 of 1353.
Sorted by year (citations)

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  1. Reeves, Alyson A.: A parallel implementation of Buchberger’s algorithm over (\mathbbZ_p) for (p\leq31991) (1998)
  2. Shin, Yong Su: The construction of some Gorenstein ideals of codimension (4) (1998)
  3. Vasconcelos, Wolmer V.: The homological degree of a module (1998)
  4. 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)
  5. 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)
  6. Boffi, G.; Bruns, W.; Guerrieri, A.: On the Jacobian ideal of a trilinear form (1997)
  7. Capani, A.; De Dominicis, G.; Niesi, G.; Robbiano, L.: Computing minimal finite free resolutions (1997)
  8. Corso, Alberto; Polini, Claudia: Reduction number of links of irreducible varieties (1997)
  9. Endrass, S.: A projective surface of degree eight with 168 nodes (1997)
  10. Geramita, Anthony V.; Migliore, Juan C.: Reduced Gorenstein codimension three subschemes of projective space (1997)
  11. Guarrera, Silvia; Logar, Alessandro; Mezzetti, Emilia: An algorithm for computing minimal curves (1997)
  12. Migliore, Juan C.; Peterson, Chris: A construction of codimension three arithmetically Gorenstein subschemes of projective space (1997)
  13. Miyazaki, Chikashi; Vogel, Wolfgang; Yanagawa, Kohji: Associated primes and arithmetic degrees (1997)
  14. Vasconcelos, Wolmer V.: Flatness testing and torsionfree morphisms (1997)
  15. Vetter, Udo; Warneke, Klaus: Differentials of a symmetric generic determinantal singularity (1997)
  16. Aslaksen, Helmer; Chan, Shih-Ping; Gulliksen, Tor: Invariants of (S_ 4) and the shape of sets of vectors (1996)
  17. Aspinwall, Paul S.; Morrison, David R.: Stable singularities in string theory (with an appendix by Mark Gross) (1996)
  18. Dana-Picard, Th.; Schaps, M.: Classifying generic algebras: The local case (1996)
  19. Drewes, R.; Stevens, J.: Deformations of cones over canonical trigonal curves (1996)
  20. Grassmann, H.; Greuel, G.-M.; Martin, B.; Neumann, W.; Pfister, G.; Pohl, W.; Schönemann, H.; Siebert, T.: On an implementation of standard bases and syzygies in SINGULAR (1996)

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