![]() ![]() In this talk, I will talk about the tools of my arsenal for printing mathematical objects, including Bertini_real, and the other programs in the tool chain. In turn, it brings the subject closer than ever to mainstream popularity. As a mathematician, this new form of fabrication can realize mathematical principles for the classroom and public consumption. As an artform, printing enables individuals to make whatever they can dream of. ![]() Printing Algebraic Geometry Daniel Brake, University of Notre DameģD printing continues to advance as a hobby and professional tool. In this talk, several of the main package contributors will give a status update of the project, with the goal of giving the audience an opportunity to influence its direction and capabilities. We will also offer methods for extending Bertini, and providing custom packages, in any supported language. Interfaces to other languages and packages are planned as well, such as Singular, Polymake, and Julia. Since it is intended for use as a library, Bertini 2 provides Python bindings for the entire body of code and aims to play nicely with as many other software packages as possible. The project goes beyond simply re-implementing with a clean interface and thorough example-driven documentation of internals. It replaces and upgrades the original C implementation of the multiprecision polynomial homotopy continuation engine. Tim Hodges, Colorado State University, andīertini 2 is the redevelopment of Bertini in C++. Invited Talks The Development of Bertini 2 Daniel Brake, University of Notre Dame, This talk will present some history, show a variety of examples from kinematic analysis and synthesis that readily yield to solution by Bertini, and discuss the rapidly rising degrees that this new tool forces us to consider. Bertini changes this by finding every solution to a polynomial system. The clever insights aren't always there and the traditional numerical methods can stumble finding just a few solutions. The standard for solving these systems was either clever geometric insights or traditional numerical methods including optimization. ![]() Problems in kinematics, from robotics to machine design, are frequently modeled by a system of algebraic equations. No prior knowledge of the area will be assumed.Īpplications of Bertini in Kinematics, Robotics, and Machine Design Andrew Murray, University of Dayton Topics for this talk will include the basics of homotopy continuation (homotopy construction, some basic theory, numerical considerations, etc.), fundamental data types such as witness sets, a brief overview of some of the more recent techniques in the field (deflation, regeneration, etc.), and a first introduction to Bertini. The goal of this talk is to introduce the fundamental concepts of numerical algebraic geometry, specifically as they are implemented in Bertini, so that workshop participants have a common language and are all on the same page. Plenary Talks Numerical Algebraic Geometry Boot Camp Daniel Bates, Colorado State University ![]()
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