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Bertini 2.0: The redevelopment of Bertini in C++.

# bertiniteam/b2

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### Important note on cloning

The recommended method for getting the code for Bertini 2 is to clone from command line using git:

git clone https://github.com/bertiniteam/b2 --recursive

This ensures that any other repo's we depend on get cloned into their correct locations.

(As of 2023, we removed the dependency that required this, but it's still good practice.)

Thanks for checking out Bertini 2!

# Overview

The solution of arbitrary polynomial systems is an area of active research, and has many applications in math, science and engineering. This program, Bertini 2, builds on the success of the first Bertini program, and seeks to eventually replace it entirely, as a powerful numerical engine.

The theoretical basis for the solution of polynomials with Bertini is a theorem which gives a statement on the number of solutions such a system may have, together with the numerical computational tool of "homotopy continuation", the act of "continuing" from one system into another through a "homotopy", as depicted in the below diagram.

# Current capabilites

Bertini2 currently has implemented the foundations of Numerical Algebraic Geometry. Development is ongoing, but here's what we have so far:

• C++ and Python bindings for access into any functionality.
• Construction of polynomial and non-polynomial multivariate systems.
• Evaluation of systems and Jacobians in double and arbitrary multiple precision.
• Construction of the Total Degree start system.
• Construction of homotopies (they're just systems with path variables defined).
• Tracking of a start point x_0, corresponding to a particular time $t_0 \in \mathbb{C}^n$ in a homotopy $H$, from $t_0$ to $t_1$.
• Running of the Power Series and Cauchy endgames.

Development is ongoing, and we want your help!

# Building and Installing

Please see the Wiki compiling section for instructions on compiling Bertini2's core library, and companion Python bindings, PyBertini.

# Other information

The offical project repository is hosted on GitHub at github.com/bertiniteam/b2.

Please note that this is a long-term project, and is under active development. If you want to help, please see the wiki for contact information. We have opportinuties for all skill levels and interests.

Bertini 2 is Free and Open Source Software. Source is available under GPL Version 3, with additional terms as permitted under Section 7.

Bertini 2.0: The redevelopment of Bertini in C++.

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