Macaulay2

Packages

• QuadraticIdealExamplesByRoos.m2
  (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.

• PossibleBettiTables.m2
  (with Juliette Bruce and Mike Loper)
  This package computes all possible Betti tables for zero-dimensional graded modules with a prescribed Hilbert function.

• 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].