Related papers: The SagbiHomotopy.jl package for solving polynomia…
We describe, study, and experiment with an algorithm for finding all solutions of systems of polynomial equations using homotopy continuation and monodromy. This algorithm follows a framework developed in previous work and can operate in…
This article introduces a software package release for geometrically reasoning about the \textit{safety} desiderata of (complex) dynamical systems via level set methods. In emphasis, safety is analyzed with Hamilton-Jacobi equations. In…
We demonstrate our implementation of a continuation method as described in \cite{HR2015} for solving polynomials systems. Given a sequence of (multi)homogeneous polynomials, the software "multiregeneration" outputs the respective…
Many applications modeled by polynomial systems have positive dimensional solution components (e.g., the path synthesis problems for four-bar mechanisms) that are challenging to compute numerically by homotopy continuation methods. A…
We present the Julia interface Polymake.jl to polymake, a software for research in polyhedral geometry. We describe the technical design and how the integration into Julia makes it possible to combine polymake with state-of-the-art…
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…
In this paper we present BilevelJuMP, a new Julia package to support bilevel optimization within the JuMP framework. The package is a Julia library that enables the user to describe both upper and lower-level optimization problems using the…
Numerical Algebraic Geometry uses numerical data to describe algebraic varieties. It is based on the methods of numerical polynomial homotopy continuation, an alternative to the classical symbolic approaches of computational algebraic…
A numerical irreducible decomposition for a polynomial system provides representations for the irreducible factors of all positive dimensional solution sets of the system, separated from its isolated solutions. Homotopy continuation methods…
The realization space of geometric constraint systems is given by the vanishing locus of polynomials corresponding to natural geometric constraints. Such geometric constraint systems arise in many real-world scenarios such as structural…
We present QuantumToolbox$.$jl, an open-source Julia package for simulating open quantum systems. Designed with a syntax familiar to users of QuTiP (Quantum Toolbox in Python), it harnesses Julia's high-performance ecosystem to deliver fast…
Efficiently solving nonlinear equations underpins numerous scientific and engineering disciplines, yet scaling these solutions for challenging system models remains a challenge. This paper presents NonlinearSolve.jl -- a suite of…
Polynomial system solving has seen major progress in both theory and practice over the past decade. A landmark achievement was addressing Smale's 17th problem, establishing average-case polynomial-time algorithms for computing approximate…
A special homotopy continuation method, as a combination of the polyhedral homotopy and the linear product homotopy, is proposed for computing all the isolated solutions to a special class of polynomial systems. The root number bound of…
The manuscript addresses the problem of finding all solutions of power flow equations or other similar nonlinear system of algebraic equations. This problem arises naturally in a number of power systems contexts, most importantly in the…
We introduce {\tt JuliBootS}, a package for numerical conformal bootstrap computations coded in {\tt Julia}. The centre-piece of {\tt JuliBootS} is an implementation of Dantzig's simplex method capable of handling arbitrary precision linear…
In this paper, we study symplectic integration of canonical Hamiltonian systems with Jacobi polynomials. The relevant theoretical results of continuous-stage Runge-Kutta methods are revisited firstly and then symplectic methods with Jacobi…
While automatically generated polynomial elimination templates have sparked great progress in the field of 3D computer vision, there remain many problems for which the degree of the constraints or the number of unknowns leads to…
Scorio.jl is a Julia package for evaluating and ranking systems from repeated responses to shared tasks. It provides a common tensor-based interface for direct score-based, pairwise, psychometric, voting, graph, and listwise methods, so the…
We present Polfed$.$jl, an open-source Julia package implementing the Polynomially Filtered Exact Diagonalization (POLFED) algorithm for computing mid-spectrum eigenvalues and eigenvectors (shortly, eigenpairs) of quantum many-body…