Macaulay2

Packages

• MixedHodgeModules.m2 (available upon request)
  (with András C. Lőrincz)
  This package is concerned with Hodge and weight filtrations on localizations S_f of the polynomial ring S at a non-constant reduced polynomial f, as well as twists S_f f^{-\alpha}, where \alpha\in (0,1] is a rational number. This includes functionality for Hodge ideals, weighted Hodge ideals, higher multiplier ideals, the generation level of Hodge filtration, and length of the weight filtration. Building upon this functionality, we include routines for graded de Rham and Du Bois complexes for hypersurfaces.

• QuadraticIdealExamplesByRoos.m2  (included with Macaulay2 version ≥1.25)
  (with David Eisenbud, Ritvik Ramkumar, Deepak Sireeshan, Aleksandra Sobieska, Teresa Yu, Jacob Zoromski)
  This package contains a list of quadratic ideals based on Main Theorem and Tables 3-7 in "Homological properties of the homology algebra of the Koszul complex of a local ring: Examples and questions" by Jan-Erik Roos, Journal of Algebra 465 (2016) 399-436. The ideals in this table exemplify 83 known cases of bi-graded Poincar\'e series of quadratic ideals of embedding dimension four in characteristic zero.

• SchurComplexes.m2 (included with Macaulay2 version ≥1.15)
  (with Michael K. Brown, Hang Huang, Robert P. Laudone, Claudiu Raicu, Steven V Sam, and João Pedro Santos)
  This package computes the Schur complex associated to a partition and a bounded complex of finitely-generated free modules over a commutative ring. An introduction to the package may be found here.

• GLmnReps.m2
  (with Claudiu Raicu)
  This package is for computations with finite-dimensional representations of the general linear Lie superalgebra and syzygies of determinantal thickenings. See also [Raicu-Weyman 2018] and [Huang 2020].