Related papers: $C_p$-Mackey functors in Macaulay2
The NumericalHilbert package for Macaulay2 includes algorithms for computing local dual spaces of polynomial ideals, and related local combinatorial data about its scheme structure. These techniques are numerically stable, and can be used…
This note describes a \emph{Macaulay2} package for computations in prime characteristic commutative algebra. This includes Frobenius powers and roots, $p^{-e}$-linear and $p^{e}$-linear maps, singularities defined in terms of these maps,…
We introduce the Brackets package for the computer algebra system Macaulay2, which provides convenient syntax for computations involving the classical invariants of the special linear group. We describe our implementation of bracket rings…
This paper describes the RationalMaps package for Macaulay2. This package provides functionality for computing several aspects of rational maps such as whether a map is birational, or a closed embedding.
We describe the computer algebra software package SpectralSequences for the computer algebra system Macaulay2. This package implements many data types, objects and algorithms which pertain to, among other things, filtered complexes,…
We compute Mackey functor-valued Tor over certain free incomplete Tambara functors, generalizing the computation of Tor over a polynomial ring on one generator. In contrast with the classical situation where the resulting Tor groups vanish…
We characterize cofibrant objects in the category of functors indexed in a filtered poset and we show that these objects are acyclic. As a consequence, we show that Mackey functors over posets are also acyclic, where we define this type of…
We introduce the DeterminantalRepresentations package for Macaulay2, which computes definite symmetric determinantal representations of real polynomials. We focus on quadrics and plane curves of low degree (i.e. cubics and quartics). Our…
We shortly describe the algorithms behind some of the functions provided by the Macaulay2 package MultiprojectiveVarieties, a package for multi-projective varieties and rational maps between them.
We introduce the \verb|Macaulay2| package \verb|RepHomology| for the computations of representation homology of certain spaces. The main methods implement computing the representation homology of surfaces (with group coefficients, and…
A supplemental paper detailing the QuillenSuslin package for Macaulay2. The QuillenSuslin package for Macaulay2 provides the ability to compute a free basis for a projective module over a polynomial ring with coefficients in Q, Z or Z/p for…
In this article, we consider a formulation of biset functors using the 2-category of finite sets with variable finite group actions. We introduce a 2-category $\mathbb{S}$, on which a biset functor can be regarded as a special kind of…
This introduces Rees algebras and some of their uses with illustrations via version 2.0 of the Macaulay2 package ReesAlgebra.m2.
We study collections of additive categories $\mathcal{M}(G)$, indexed by finite groups $G$ and related by induction and restriction in a way that categorifies usual Mackey functors. We call them `Mackey 2-functors'. We provide a large…
We introduce the Macaulay2 package $\mathtt{LinearTruncations}$ for finding and studying the truncations of a multigraded module over a standard multigraded ring that have linear resolutions.
The Macaulay2 package CharacteristicClasses provides commands for the computation of the topological Euler characteristic, the degrees of the Chern classes and the degrees of the Segre classes of a closed subscheme of complex projective…
We introduce a Macaulay2 package for working with jet schemes. The main method constructs jets of ideals, polynomial rings and their quotients, ring homomorphisms, affine varieties, and (hyper)graphs. The package also includes additional…
In equivariant algebra, Mackey functors replace abelian groups and incomplete Tambara functors replace commutative rings. In this context, we prove that equivariant Hochschild homology can sometimes be computed using Mackey functor-valued…
We introduce the VirtualResolution package for the computer algebra system Macaulay2. This package has tools to construct, display, and study virtual resolutions for products of projective spaces. The package also has tools for generating…
The {\tt Macaulay2} package {\tt RandomMonomialIdeals} provides users with a set of tools that allow for the systematic generation and study of random monomial ideals. It also introduces new objects, Sample and Model, to allow for…