We present the Julia package HomotopyContinuation. jl, which provides an algorithmic
framework for solving polynomial systems by numerical homotopy continuation. We …

In this article, the basic constructs of algebraic kinematics (links, joints, and mechanism
spaces) are introduced. This provides a common schema for many kinds of problems that …

Abstract HOM4PS-2.0 is a software package in FORTRAN 90 which implements the
polyhedral homotopy continuation method for solving polynomial systems. It updates its …

Smale's α-theory uses estimates related to the convergence of Newton's method to certify
that Newton iterations will converge quadratically to solutions to a square polynomial …

The manuscript addresses the problem of finding all solutions of power flow equations or
other similar non‐linear system of algebraic equations. This problem arises naturally in a …

We consider the Bethe equations for the isotropic spin-1/2 Heisenberg quantum spin chain
with periodic boundary conditions. We formulate a conjecture for the number of solutions …

We present a new technique, based on polynomial continuation, for solving systems of $ n $
polynomials in $ N $ complex variables. The method allows equations to be introduced one …

We propose a new algorithm for numerical path tracking in polynomial homotopy
continuation. The algorithm is “robust” in the sense that it is designed to prevent path …

Designing and analyzing large cable-driven parallel robots (CDPRs) for precision tasks can
be challenging, as the position kinematics are governed by kineto-statics and cable sag …

Given a polynomial system f, a fundamental question is to determine if f has real roots. Many
algorithms involving the use of infinitesimal deformations have been proposed to answer …