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 961 articles , 2 standard articles )

Showing results 1 to 20 of 961.
Sorted by year (citations)

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  1. Alesandroni, Guillermo: Minimal resolutions of dominant and semidominant ideals (2017)
  2. Aluffi, Paolo: How many hypersurfaces does it take to cut out a Segre class? (2017)
  3. Banerjee, Arindam; Núñez-Betancourt, Luis: Graph connectivity and binomial edge ideals (2017)
  4. Blekherman, Grigoriy; Sinn, Rainer: Extreme rays of Hankel spectrahedra for ternary forms (2017)
  5. Bouchat, Rachelle R.; Brown, Tricia Muldoon: Multi-graded Betti numbers of path ideals of trees (2017)
  6. Brinkmann, Daniel: The Hilbert-Kunz functions of two-dimensional rings of type ADE (2017)
  7. de Alba, Hernán; Morales, Marcel: Betti numbers of binomial ideals (2017)
  8. DiPasquale, Michael: Generalized splines and graphic arrangements (2017)
  9. Galetto, Federico: Generators of truncated symmetric polynomials (2017)
  10. Harris, Corey: Computing Segre classes in arbitrary projective varieties (2017)
  11. Hernández, Daniel J.; Teixeira, Pedro: $F$-threshold functions: Syzygy gap fractals and the two-variable homogeneous case (2017)
  12. Horobeţ, Emil; Rodriguez, Jose Israel: The maximum likelihood data singular locus (2017)
  13. Janko Boehm, Wolfram Decker, Simon Keicher, Yue Ren: Current Challenges in Developing Open Source Computer Algebra Systems (2017) arXiv
  14. Krone, Robert; Leykin, Anton: Eliminating dual spaces (2017)
  15. Krone, Robert; Leykin, Anton: Numerical algorithms for detecting embedded components (2017)
  16. Kustin, Andrew R.; Polini, Claudia; Ulrich, Bernd: A matrix of linear forms which is annihilated by a vector of indeterminates (2017)
  17. Lee, Hwangrae: The Euclidean distance degree of Fermat hypersurfaces (2017)
  18. Mahdi, Adam; Pessoa, Claudio; Hauenstein, Jonathan D.: A hybrid symbolic-numerical approach to the center-focus problem (2017)
  19. Martín del Campo, Abraham; Rodriguez, Jose Israel: Critical points via monodromy and local methods (2017)
  20. Miranda-Neto, Cleto B.: On Aluffi’s problem and blowup algebras of certain modules (2017)

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