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 1808 articles , 2 standard articles )

Showing results 1 to 20 of 1808.
Sorted by year (citations)

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  1. Améndola, Carlos; Pham, Viet Son: Autocovariance varieties of moving average random fields (2022)
  2. Angelini, Elena; Bocci, Cristiano; Chiantini, Luca: Catalecticant intersections and confinement of decompositions of forms (2022)
  3. Banerjee, Arindam; Chakraborty, Bidwan; Das, Kanoy Kumar; Mandal, Mousumi; Selvaraja, S.: Regularity of powers of squarefree monomial ideals (2022)
  4. Bopp, Christian; Hoff, Michael: Moduli of lattice polarized (K3) surfaces via relative canonical resolutions (2022)
  5. Cifuentes, Diego; Ranestad, Kristian; Sturmfels, Bernd; Weinstein, Madeleine: Voronoi cells of varieties (2022)
  6. Duff, Timothy; Hein, Nickolas; Sottile, Frank: Certification for polynomial systems via square subsystems (2022)
  7. Galeano, Hugo; Jardim, Marcos; Muniz, Alan: Codimension one distributions of degree 2 on the three-dimensional projective space (2022)
  8. Jafari, Raheleh; Yaghmaei, Marjan: Type and conductor of simplicial affine semigroups (2022)
  9. Kudo, Momonari: Computing representation matrices for the action of Frobenius on cohomology groups (2022)
  10. Park, Euisung: On surfaces of minimal degree in (\mathbbP^5) (2022)
  11. Ramkumar, Ritvik; Sammartano, Alessio: On the smoothness of lexicographic points on Hilbert schemes (2022)
  12. Abuaf, Roland: On quartic double fivefolds and the matrix factorizations of exceptional quaternionic representations (2021)
  13. Addington, Nicolas; Wray, Andrew: Twisted Fourier-Mukai partners of Enriques surfaces (2021)
  14. Agostini, Daniele; Améndola, Carlos; Ranestad, Kristian: Moment identifiability of homoscedastic Gaussian mixtures (2021)
  15. Agostini, Daniele; Barros, Ignacio: Pencils on surfaces with normal crossings and the Kodaira dimension of (\overline\mathcalM_g,n) (2021)
  16. Agostini, Daniele; Chua, Lynn: On the Schottky problem for genus five Jacobians with a vanishing theta null (2021)
  17. Ansaldi, Katie; Lin, Kuei-Nuan; Shen, Yi-Huang: Generalized Newton complementary duals of monomial ideals (2021)
  18. Arrondo, Enrique; Bernardi, Alessandra; Marques, Pedro Macias; Mourrain, Bernard: Skew-symmetric tensor decomposition (2021)
  19. Asgarli, Shamil; Duan, Lian; Lai, Kuan-Wen: Transverse lines to surfaces over finite fields (2021)
  20. Ballico, Edoardo; Favacchio, Giuseppe; Guardo, Elena; Milazzo, Lorenzo: Steiner systems and configurations of points (2021)

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