Computational contributions:

• TSpreadIdeals arXiv
  GitHub
  a Macaulay2 package for creating and manipulating t-spread ideals of polynomial rings.
  Macaulay2
  Details

  This package includes some methods to manage stable and strongly stable $t$-spread ideals and to compute the lexicographic $t$-spread ideal with the same $f_t$-vector of a given strongly stable ideal through a generalization of the Kruskal–Katona theorem. Moreover, some methods allow to give a numerical characterization of the extremal Betti numbers of $t$-spread strongly stable ideals of a polynomial ring and to compute $t$-spread strongly stable ideals with given extremal Betti numbers (positions as well as values).
• ExteriorModules journal
  GitHub
  a Macaulay2 package for creating and manipulating modules over an exterior algebra.
  Macaulay2
  Details

  This package includes some methods to manage stable and strongly stable modules and to compute the lexicographic submodule of the ambient module with the same Hilbert function of a given graded submodule through a generalization of the Kruskal–Katona theorem (or through an alternative algorithm).
• ExteriorIdeals journal
  GitHub
  a Macaulay2 package for creating and manipulating ideals of an exterior algebra.
  Macaulay2
  Details

  This package includes some methods to manage stable and strongly stable ideals and to compute the lexicographic ideal with the same Hilbert function of a given graded ideal through the Kruskal–Katona theorem.
• SquarefreeIdeals journal
  a Macaulay2 package for creating and manipulating squarefree ideals of polynomial rings.
  Details

  This package includes some methods to manage stable and strongly stable squarefree ideals and to compute the lexicographic squarefree ideal with the same Hilbert function of a given graded ideal through the Kruskal–Katona theorem. Moreover, some methods allow to give a numerical characterization of the extremal Betti numbers of squarefree graded ideals of a polynomial ring and to compute squarefree strongly stable ideals with given extremal Betti numbers (positions as well as values).
• GenericInitialModules (in progress) GitHub
  a Macaulay2 package for computing the generic initial module of a graded module over a graded algebra.
• ExtrBettiNumbers journal
  source
  a CoCoA package for compute graded ideals of a polynomial ring with given extremal Betti numbers.
  Details

  Consider a polynomial ring in a finite number of variables over a field of characteristic $0$. We implement in CoCoA some algorithms in order to easy compute graded ideals of this ring with given extremal Betti numbers (positions as well as values). More precisely, we develop a package for determining the conditions under which, given two positive integers $n, r$, $1\le r \le n-1$, there exists a graded ideal of a polynomial ring in $n$ variables with $r$ extremal Betti numbers in the given position. An algorithm to check whether an $r$-tuple of positive integers represents the admissible values of the $r$ extremal Betti numbers is also described. An example in order to show how the package works is also presented.