Related papers: Computing Schur complexes
The nn2poly package provides the implementation in R of the NN2Poly method to explain and interpret feed-forward neural networks by means of polynomial representations that predict in an equivalent manner as the original network.Through the…
This preprint contains a description of a package for Mathematica called EinS. This package allows one to perform various calculations with indexed objects.
In this article we survey recent results on rigid dualizing complexes over commutative algebras. We begin by recalling what are dualizing complexes. Next we define rigid complexes, and explain their functorial properties. Due to the…
We describe the Macaulay2 package TateOnProducts and its capabilities, which include computing cohomology tables and Beilinson monads of sheaves on products of projective spaces and the derived category pushForward of a sheaf under a…
We introduce the Macaulay2 package ThinSincereQuivers for studying acyclic quivers, the moduli of their thin-sincere representations, and the reflexive flow polytopes associated to them. We provide some background on the topic and…
The Macaulay2 package PHCpack.m2 provides an interface to PHCpack, a general-purpose polynomial system solver that uses homotopy continuation. The main method is a numerical blackbox solver which is implemented for all Laurent systems. The…
A method is presented for using coherent vectors to calculate the explicit form of Schur polynomials which are the coefficients of Laurent expansion of a vertex operator.
The program package XLOOPS calculates massive one- and two-loop Feynman diagrams. It consists of five parts: i) a graphical user interface ii) routines for generating diagrams from particle input iii) procedures for calculating one-loop…
A set of recurrence relations for on-shell two-loop self-energy diagrams with one mass is presented, which allows to reduce the diagrams with arbitrary indices (powers of scalar propagators) to a set of the master integrals. The SHELL2…
Based on computeralgebra experiments we formulate a refined version of Green's conjecture and a conjecture of Schicho-Schreyer-Weimann which conjecturally also holds in positive characteristic. The experiments are done by using our…
This paper develops techniques for producing presentations of upper cluster algebras. These techniques are suited to computer implementation, and will always succeed when the upper cluster algebra is totally coprime and finitely generated.…
Symbolic powers are a classical commutative algebra topic that relates to primary decomposition, consisting, in some circumstances, of the functions that vanish up to a certain order on a given variety. However, these are notoriously…
Mixed integer sets have a strong modeling capacity to describe practical systems. Nevertheless, incorporating a mixed integer set often renders an optimization formulation drastically more challenging to compute. In this paper, we study how…
Solving a system of polynomial equations is a ubiquitous problem in the applications of mathematics. Until recently, it has been hopeless to find explicit solutions to such systems, and mathematics has instead developed deep and powerful…
We describe a general purpose Mathematica package for computing Superfield Operator Product Expansions in meromorphic $N=2$ superconformal field theory. Given the SOPEs for a set of ``basic" superfields, SOPEs of arbitrarily complicated…
The dirichletprocess package provides software for creating flexible Dirichlet process objects. Users can perform nonparametric Bayesian analysis using Dirichlet processes without the need to program their own inference algorithms. Instead,…
In the package corr2D two-dimensional correlation analysis is implemented in R. This paper describes how two-dimensional correlation analysis is done in the package and how the mathematical equations are translated into R code. The paper…
We present a Julia package HypersurfaceRegions.jl for computing all connected components in the complement of an arrangement of real algebraic hypersurfaces in $\mathbb{R}^n$.
Coupled multi-physics problems are encountered in countless applications and pose significant numerical challenges. Although monolithic approaches offer possibly the best solution strategy, they often require ad-hoc preconditioners and…
We describe a recently revived version of the software package SubalgberaBases, which is distributed in the Macaulay2 computer algebra system. The package allows the user to compute and manipulate subagebra bases -- which are also known as…