相关论文: Nauty in Macaulay2

This note introduces the Macaulay2 package SchurVeronese, which gathers together data about Veronese syzygies and makes it readily accessible in Macaulay2. In addition to standard Betti tables, the package includes information about the…

This introduces Rees algebras and some of their uses with illustrations via version 2.0 of the Macaulay2 package ReesAlgebra.m2.

Simflowny is an open platform which automatically generates parallel code of scientific dynamical models for different simulation frameworks. Here we present major upgrades on this software to support an extended set of families of models,…

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 introduce the Macaulay2 package SparseResultants, which provides general tools for computing sparse resultants, sparse discriminants, and hyperdeterminants. We give some background on the theory and briefly show how the package works.

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 describe a Macaulay2 package for computing Schur complexes. This package expands on the ChainComplexOperations package by David Eisenbud.

We introduce the Macaulay2 package SCMAlgebras. It provides functions for computing the modules of deficiency and the filter ideals, in order to check whether a module or an ideal is sequentially Cohen-Macaulay. After the basic algebraic…

In this Macaulay2 \cite{M2} package we define an object called {\it linear code}. We implement functions that compute basic parameters and objects associated with a linear code, such as generator and parity check matrices, the dual code,…

We present the $\textit{NumericalImplicitization}$ package for $\textit{Macaulay2}$, which allows for user-friendly computation of the invariants of the image of a polynomial map, such as dimension, degree, and Hilbert function values. This…

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…

Symmetry in mathematical programming may lead to a multiplicity of solutions. In nonconvex optimisation, it can negatively affect the performance of the branch-and-bound algorithm. Symmetry may induce large search trees with multiple…

This tutorial illustrates how to use Grayson and Stillman's computer algebra system, Macaulay2, to study schemes. The examples are taken from the homework for an algebraic geometry class given at the University of California, Berkeley in…

We present bipartiteSUSY, a Mathematica package designed to perform calculations for physical theories based on bipartite graphs. In particular, the package can employ the recently developed arsenal of techniques surrounding on-shell…

Networks provide a meaningful way to represent and analyze complex biological information, but the methodological details of network-based tools are often described for a technical audience. Graphery is a hands-on tutorial webserver…

We provide an overview of the Macaulay2 package VersalDeformations, which algorithmically computes versal deformations of isolated singularities, as well as local (multi)graded Hilbert schemes.

We introduce Lagrange2D, a Mathematica package for analysis and characterization of complex fluid flows using Lagrangian transport metrics. Lagrange2D includes built-in functions for integrating ensembles of trajectories subject to…

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 introduce GraSPy, a Python library devoted to statistical inference, machine learning, and visualization of random graphs and graph populations. This package provides flexible and easy-to-use algorithms for analyzing and understanding…

This note describes a package for computing seminormalization of rings within Macaulay2.