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 1321 to 1340 of 1353.
Sorted by year (citations)

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  1. Greuel, G.-M.; Pfister, G.: Advances and improvements in the theory of standard bases and syzygies (1996)
  2. Kemper, Gregor: Calculating invariant rings of finite groups over arbitrary fields (1996)
  3. Morey, Susan: Equations of blowups of ideals of codimension two and three (1996)
  4. Roos, Jan-Erik: On computer-assisted research in homological algebra. (1996)
  5. Roos, Jan-Erik: On computer-assisted research in homological algebra. (1996) ioport
  6. Schreyer, Frank-Olaf: Small fields in constructive algebraic geometry (1996)
  7. Stevens, J.: On the computation of versal deformations (1996)
  8. Vasconcelos, Wolmer V.: The reduction number of an algebra (1996)
  9. Bayer, Dave; Eisenbud, David: Ribbons and their canonical embeddings (1995)
  10. Decker, Wolfram; Popescu, Sorin: On surfaces in (\mathbbP^ 4) and 3-folds in (\mathbbP^ 5) (1995)
  11. Migliore, Juan C.; Nagel, Uwe: On the Cohen-Macaulay type of the general hypersurface section of a curve (1995)
  12. Björck, Göran; Fröberg, Ralf: Methods to “divide out” certain solutions from systems of algebraic equations, applied to find all cyclic 8-roots (1994)
  13. Fröberg, Ralf; Hollman, Joachim: Hilbert series for ideals generated by generic forms (1994)
  14. Haiman, Mark D.: Conjectures on the quotient ring by diagonal invariants (1994)
  15. Iarrobino, Anthony A.: Associated graded algebra of a Gorenstein Artin algebra (1994)
  16. Roos, Jan-Erik: A computer-aided study of the graded Lie algebra of a local commutative noetherian ring. -- Appendix A: Some technical details about how the computer was used. -- Appendix B (by Clas Löfwall): The Lie algebra structure of a ring satisfying (\mathcalM_ 3) and variants (1994)
  17. Xu, Changsheng: Computing invariant polynomials of (p)-adic reflection groups (1994)
  18. Brundu, Michela; Stillman, Mike: Computing the equations of a variety (1993)
  19. Noh, Sunsook; Vasconcelos, Wolmer V.: The (S_ 2)-closure of a Rees algebra (1993)
  20. Stevens, J.: The versal deformation of universal curve singularities (1993)

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