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 1576 articles , 2 standard articles )

Showing results 61 to 80 of 1576.
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  1. Mohammadi, Fatemeh; Pascual-Ortigosa, Patricia; Sáenz-de-Cabezón, Eduardo; Wynn, Henry P.: Polarization and depolarization of monomial ideals with application to multi-state system reliability (2020)
  2. Nützi, Andrea; Reiterer, Michael: Scattering amplitude annihilators (2020)
  3. Rennemo, Jørgen Vold: The homological projective dual of (\operatornameSym^2\mathbbP(V)) (2020)
  4. Romeo, Francesco: Chordal circulant graphs and induced matching number (2020)
  5. Sammartano, Alessio: Blowup algebras of rational normal scrolls (2020)
  6. Saremi, Hero; Mafi, Amir: Unmixedness and arithmetic properties of matroidal ideals (2020)
  7. Sarkar, Parangama: Rees’ theorem for filtrations, multiplicity function and reduction criteria (2020)
  8. Schwede, Karl; Serbinowski, Bernard: Seminormalization package for Macaulay2 (2020)
  9. Shibuta, Takafumi; Tajima, Shinichi: An algorithm for computing the Hilbert-Samuel multiplicities and reductions of zero-dimensional ideals of Cohen-Macaulay local rings (2020)
  10. Sordo Vieira, Luis; Laubenbacher, Reinhard C.; Murrugarra, David: Control of intracellular molecular networks using algebraic methods (2020)
  11. Staglianò, Giovanni: Special cubic birational transformations of projective spaces (2020)
  12. Telen, Simon: Numerical root finding via Cox rings (2020)
  13. Tohǎneanu, Ştefan O.; Xie, Yu: On the containment problem for fat points ideals and Harbourne’s conjecture (2020)
  14. Toshniwal, Deepesh; Villamizar, Nelly: Dimension of polynomial splines of mixed smoothness on T-meshes (2020)
  15. Trung, Dinh Thanh: On the computation of Castelnuovo-Mumford regularity of the Rees algebra and of the fiber ring (2020)
  16. Trung, Tran Nam: Regularity, matchings and Cameron-Walker graphs (2020)
  17. Winther Christensen, Lars; Veliche, Oana; Weyman, Jerzy: Linkage classes of grade 3 perfect ideals (2020)
  18. Abdi Makvand, Mohsen; Mousivand, Amir: Betti numbers of some circulant graphs. (2019)
  19. Ahn, Jeaman; Kwak, Sijong: The regularity of partial elimination ideals, Castelnuovo normality and syzygies (2019)
  20. Al-Ayyoub, Ibrahim; Nasernejad, Mehrdad; Roberts, Leslie G.: Normality of cover ideals of graphs and normality under some operations (2019)

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