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 1160 articles , 2 standard articles )

Showing results 1 to 20 of 1160.
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  1. Ahn, Jeaman; Migliore, Juan C.; Shin, Yong-Su: Green’s theorem and Gorenstein sequences (2018)
  2. Alilooee, A.; Faridi, S.: Graded Betti numbers of path ideals of cycles and lines (2018)
  3. Angelini, Elena; Galuppi, Francesco; Mella, Massimiliano; Ottaviani, Giorgio: On the number of Waring decompositions for a generic polynomial vector (2018)
  4. Annunziata, Michael T.; Gibbons, Courtney R.; Hawkins, Cole; Sutherland, Alexander J.: Rational combinations of Betti diagrams of complete intersections (2018)
  5. Benedetti, Bruno; Di Marca, Michela; Varbaro, Matteo: Regularity of line configurations (2018)
  6. Berest, Yuri; Samuelson, Peter: Affine cubic surfaces and character varieties of knots (2018)
  7. Bernardi, Alessandra; Gimigliano, Alessandro; Idà, Monica: Singularities of plane rational curves via projections (2018)
  8. Blanco-Chacón, Iván; Boix, Alberto F.; Fordham, Stiofáin; Yilmaz, Emrah Sercan: Differential operators and hyperelliptic curves over finite fields (2018)
  9. Böhm, Janko; Frühbis-Krüger, Anne: A smoothness test for higher codimensions (2018)
  10. Boij, Mats; Fröberg, Ralf; Lundqvist, Samuel: Powers of generic ideals and the weak Lefschetz property for powers of some monomial complete intersections (2018)
  11. Bolognesi, Michele; Massarenti, Alex: Varieties of sums of powers and moduli spaces of $(1,7)$-polarized abelian surfaces (2018)
  12. Bolognini, Davide; Macchia, Antonio; Strazzanti, Francesco: Binomial edge ideals of bipartite graphs (2018)
  13. Brown, Gavin; Kasprzyk, Alexander M.; Qureshi, Muhammad Imran: Fano 3-folds in $\mathbbP^2\times\mathbbP^2$ format, Tom and Jerry (2018)
  14. Bydlon, Andrew: Counterexamples to Bertini theorems for test ideals (2018)
  15. Cohen, Daniel C.: Topological complexity of classical configuration spaces and related objects (2018)
  16. Coss, Owen; Hauenstein, Jonathan D.; Hong, Hoon; Molzahn, Daniel K.: Locating and counting equilibria of the Kuramoto model with rank-one coupling (2018)
  17. Costa, L.; Marchesi, S.; Miró-Roig, R. M.: A Horrocks’ theorem for reflexive sheaves (2018)
  18. Dipasquale, Michael: Dimension of mixed splines on polytopal cells (2018)
  19. Fløystad, Gunnar; Kileel, Joe; Ottaviani, Giorgio: The Chow form of the essential variety in computer vision (2018)
  20. Fontanari, Claudio; Ghiloni, Riccardo; Lella, Paolo: A computational approach to the ample cone of moduli spaces of curves (2018)

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