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 1260 articles , 2 standard articles )

Showing results 1 to 20 of 1260.
Sorted by year (citations)

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  1. Améndola, Carlos; Bliss, Nathan; Burke, Isaac; Gibbons, Courtney R.; Helmer, Martin; Hoşten, Serkan; Nash, Evan D.; Rodriguez, Jose Israel; Smolkin, Daniel: The maximum likelihood degree of toric varieties (2019-2019)
  2. Almeida, Charles; Andrade, Aline V.; Miró-Roig, Rosa M.: Gaps in the number of generators of monomial Togliatti systems (2019)
  3. Angelini, Elena: Waring decompositions and identifiability via Bertini and Macaulay2 software (2019)
  4. Chan, Andrew J.; Maclagan, Diane: Gröbner bases over fields with valuations (2019)
  5. Cueto, Maria Angelica; Markwig, Hannah: Tropical geometry of genus two curves (2019)
  6. De Loera, Jesús A.; Petrović, Sonja; Silverstein, Lily; Stasi, Despina; Wilburne, Dane: Random monomial ideals (2019)
  7. Erman, Daniel; Sam, Steven V.; Snowden, Andrew: Cubics in 10 variables vs. cubics in 1000 variables: uniformity phenomena for bounded degree polynomials (2019)
  8. Faenzi, Daniele; Polizzi, Francesco; Vallès, Jean: Triple planes with $p_g=q=0$ (2019)
  9. Mayes-Tang, Sarah: Stabilization of Boij-Söderberg decompositions of ideal powers (2019)
  10. Abe, Hiraku; DeDieu, Lauren; Galetto, Federico; Harada, Megumi: Geometry of Hessenberg varieties with applications to Newton-Okounkov bodies (2018)
  11. Addington, Nicolas; Auel, Asher: Some non-special cubic fourfolds (2018)
  12. Ahn, Jeaman; Migliore, Juan C.; Shin, Yong-Su: Green’s theorem and Gorenstein sequences (2018)
  13. Alesandroni, Guillermo: Structural decomposition of monomial resolutions (2018)
  14. Alfaro, Carlos A.: Graphs with real algebraic co-rank at most two (2018)
  15. Alfaro, Carlos A.; Valencia, Carlos E.: Small clique number graphs with three trivial critical ideals (2018)
  16. Alilooee, A.; Faridi, S.: Graded Betti numbers of path ideals of cycles and lines (2018)
  17. Alilooee, Ali; Soprunov, Ivan; Validashti, Javid: Generalized multiplicities of edge ideals (2018)
  18. Angelini, Elena; Galuppi, Francesco; Mella, Massimiliano; Ottaviani, Giorgio: On the number of Waring decompositions for a generic polynomial vector (2018)
  19. Annunziata, Michael T.; Gibbons, Courtney R.; Hawkins, Cole; Sutherland, Alexander J.: Rational combinations of Betti diagrams of complete intersections (2018)
  20. Baker, Jonathan; Vander Meulen, Kevin N.; Van Tuyl, Adam: Shedding vertices of vertex decomposable well-covered graphs (2018)

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