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 1023 articles , 2 standard articles )

Showing results 1 to 20 of 1023.
Sorted by year (citations)

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  1. Ahn, Jeaman; Migliore, Juan C.; Shin, Yong-Su: Green’s theorem and Gorenstein sequences (2018)
  2. Genc, Ozhan: Stable Ulrich bundles on Fano threefolds with Picard number 2 (2018)
  3. Alesandroni, Guillermo: Minimal resolutions of dominant and semidominant ideals (2017)
  4. Aluffi, Paolo: How many hypersurfaces does it take to cut out a Segre class? (2017)
  5. Aprodu, Marian; Kim, Yeongrak: Ulrich line bundles on Enriques surfaces with a polarization of degree four (2017)
  6. Banerjee, Arindam; Núñez-Betancourt, Luis: Graph connectivity and binomial edge ideals (2017)
  7. Bigatti, Anna M. (ed.); Gimenez, Philippe (ed.); Sáenz-de-Cabezón, Eduardo (ed.): Computations and combinatorics in commutative algebra. EACA school, Valladolid, Spain, 2013 (2017)
  8. Blekherman, Grigoriy; Sinn, Rainer: Extreme rays of Hankel spectrahedra for ternary forms (2017)
  9. Bouchat, Rachelle R.; Brown, Tricia Muldoon: Multi-graded Betti numbers of path ideals of trees (2017)
  10. Brinkmann, Daniel: The Hilbert-Kunz functions of two-dimensional rings of type ADE (2017)
  11. Bruns, Winfried; Conca, Aldo: Products of Borel fixed ideals of maximal minors (2017)
  12. Bruns, Winfried; Conca, Aldo: Linear resolutions of powers and products (2017)
  13. Carlini, Enrico; Catalisano, Maria Virginia; Oneto, Alessandro: Waring loci and the Strassen conjecture (2017)
  14. Chen, Justin; Kim, Youngsu: Graded-irreducible modules are irreducible (2017)
  15. Chiantini, Luca; Ottaviani, Giorgio; Vannieuwenhoven, Nick: On generic identifiability of symmetric tensors of subgeneric rank (2017)
  16. Curto, Carina; Gross, Elizabeth; Jeffries, Jack; Morrison, Katherine; Omar, Mohamed; Rosen, Zvi; Shiu, Anne; Youngs, Nora: What makes a neural code convex? (2017)
  17. Dall, Aaron: Internally perfect matroids (2017)
  18. David Kahle, Christopher O’Neill, Jeff Sommars: A computer algebra system for R: Macaulay2 and the m2r package (2017) arXiv
  19. de Alba, Hernán; Morales, Marcel: Betti numbers of binomial ideals (2017)
  20. DiPasquale, Michael: Generalized splines and graphic arrangements (2017)

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