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 1122 articles , 2 standard articles )

Showing results 1 to 20 of 1122.
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  1. Ahn, Jeaman; Migliore, Juan C.; Shin, Yong-Su: Green’s theorem and Gorenstein sequences (2018)
  2. Angelini, Elena; Galuppi, Francesco; Mella, Massimiliano; Ottaviani, Giorgio: On the number of Waring decompositions for a generic polynomial vector (2018)
  3. Bernardi, Alessandra; Gimigliano, Alessandro; Idà, Monica: Singularities of plane rational curves via projections (2018)
  4. Böhm, Janko; Frühbis-Krüger, Anne: A smoothness test for higher codimensions (2018)
  5. Boij, Mats; Fröberg, Ralf; Lundqvist, Samuel: Powers of generic ideals and the weak Lefschetz property for powers of some monomial complete intersections (2018)
  6. Dipasquale, Michael: Dimension of mixed splines on polytopal cells (2018)
  7. Fløystad, Gunnar; Kileel, Joe; Ottaviani, Giorgio: The Chow form of the essential variety in computer vision (2018)
  8. García-García, J.I.; Moreno-Frías, M.A.; Vigneron-Tenorio, A.: Proportionally modular affine semigroups (2018)
  9. Genc, Ozhan: Stable Ulrich bundles on Fano threefolds with Picard number 2 (2018)
  10. Gross, Elizabeth; Obatake, Nida; Youngs, Nora: Neural ideals and stimulus space visualization (2018)
  11. Kadyrsizova, Zhibek: Nearly commuting matrices (2018)
  12. Kleppe, Jan O.: Families of Artinian and low dimensional determinantal rings (2018)
  13. Massarenti, Alex; Mella, Massimiliano; Staglianò, Giovanni: Effective identifiability criteria for tensors and polynomials (2018)
  14. Nødland, Bernt Ivar Utstøl: Local Euler obstructions of toric varieties (2018)
  15. Römer, Tim; Saeedi Madani, Sara: Retracts and algebraic properties of cut algebras (2018)
  16. Torrente, Maria-Laura; Varbaro, Matteo: Computing the Betti table of a monomial ideal: a reduction algorithm (2018)
  17. Tran, Quang Hoa: Bound for the number of one-dimensional fibers of a projective morphism (2018)
  18. Zhang, Xiping: Chern classes and characteristic cycles of determinantal varieties (2018)
  19. Alesandroni, Guillermo: Minimal resolutions of dominant and semidominant ideals (2017)
  20. Aluffi, Paolo: How many hypersurfaces does it take to cut out a Segre class? (2017)

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