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 1214 articles , 2 standard articles )

Showing results 1 to 20 of 1214.
Sorted by year (citations)

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  1. Abe, Hiraku; DeDieu, Lauren; Galetto, Federico; Harada, Megumi: Geometry of Hessenberg varieties with applications to Newton-Okounkov bodies (2018)
  2. Addington, Nicolas; Auel, Asher: Some non-special cubic fourfolds (2018)
  3. Ahn, Jeaman; Migliore, Juan C.; Shin, Yong-Su: Green’s theorem and Gorenstein sequences (2018)
  4. Alfaro, Carlos A.: Graphs with real algebraic co-rank at most two (2018)
  5. Alfaro, Carlos A.; Valencia, Carlos E.: Small clique number graphs with three trivial critical ideals (2018)
  6. Alilooee, A.; Faridi, S.: Graded Betti numbers of path ideals of cycles and lines (2018)
  7. Alilooee, Ali; Soprunov, Ivan; Validashti, Javid: Generalized multiplicities of edge ideals (2018)
  8. Angelini, Elena; Galuppi, Francesco; Mella, Massimiliano; Ottaviani, Giorgio: On the number of Waring decompositions for a generic polynomial vector (2018)
  9. Annunziata, Michael T.; Gibbons, Courtney R.; Hawkins, Cole; Sutherland, Alexander J.: Rational combinations of Betti diagrams of complete intersections (2018)
  10. Ballico, E.; Callander, B.; Gasparim, E.: Compactifications of adjoint orbits and their Hodge diamonds (2018)
  11. Benedetti, Bruno; Di Marca, Michela; Varbaro, Matteo: Regularity of line configurations (2018)
  12. Berest, Yuri; Samuelson, Peter: Affine cubic surfaces and character varieties of knots (2018)
  13. Berget, Andrew: Internal zonotopal algebras and the monomial reflection groups $G(m,1,n)$ (2018)
  14. Berget, Andrew; Fink, Alex: Matrix orbit closures (2018)
  15. Bernardi, Alessandra; Gimigliano, Alessandro; Idà, Monica: Singularities of plane rational curves via projections (2018)
  16. Blanco-Chacón, Iván; Boix, Alberto F.; Fordham, Stiofáin; Yilmaz, Emrah Sercan: Differential operators and hyperelliptic curves over finite fields (2018)
  17. Böhm, Janko; Frühbis-Krüger, Anne: A smoothness test for higher codimensions (2018)
  18. Boij, Mats; Fröberg, Ralf; Lundqvist, Samuel: Powers of generic ideals and the weak Lefschetz property for powers of some monomial complete intersections (2018)
  19. Boij, Mats; Migliore, Juan; Miró-Roig, Rosa M.; Nagel, Uwe: The non-Lefschetz locus (2018)
  20. Bolognesi, Michele; Massarenti, Alex: Varieties of sums of powers and moduli spaces of $(1,7)$-polarized abelian surfaces (2018)

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