Coefficient-parameter polynomial continuation

TL;DR: The Numerical Continuation Methods for Nonlinear Systems of Equations (NCME) as discussed by the authors is an excellent introduction to numerical continuuation methods for solving nonlinear systems of equations.

TL;DR: The structure and design of the software package PHC is described, which features great variety of root-counting methods among its tools and is ensured by the gnu-ada compiler.

TL;DR: This revision of HOM4PS-2.0 updates its original version in three key aspects: (1) new method for finding mixed cells, (2) combining the polyhedral and linear homotopies in one step, (3) new way of dealing with curve jumping.

TL;DR: The algorithm for computing the BKK bound for the number of isolated solutions of a polynomial system with a sparse monomial structure is described and the algorithmic construction of the cheater’s homotopy or the coefficienthomotopy is obtained.

TL;DR: In this paper, the Riemann-Roch theorem for algebraic manifolds and complex analytic vector bundles is presented. But the authors do not consider the complexity of complex analytic line bundles.

TL;DR: The theory of analytic functions of several complex variables enjoyed a period of remarkable development in the middle part of the twentieth century after initial successes by Poincare and others in the late 19th and early 20th centuries, the theory encountered obstacles that prevented it from growing quickly into an analogue of the theory for functions of one complex variable as discussed by the authors.

TL;DR: In this article, the authors discuss the properties of holomorphic functions of complex vectors in more detail, including their properties with respect to their properties in the context of complex vector models.