Bertini™: Software for
Numerical Algebraic Geometry
Software for solving polynomial systems
Facts in brief:
- Purpose: The numerical solution
of systems of polynomial equations
- Approach: Homotopy
- Authors: Daniel J.
D. Hauenstein, Andrew J. Sommese, Charles W. Wampler
- Background: Bertini
is a general-purpose solver, written in C, that
was created for research about polynomial continuation.
- Cost: Bertini
is distributed free of charge on an ``as is'' basis with no warranties,
implied or otherwise, that it is suitable for any purpose. Its intended
usage is educational, so that the user may gain a greater understanding of
numerical homotopy continuation for solving
systems of polynomial equations. Any other use is strictly the user's
responsibility. Please see the official license policy.
- Finds isolated solutions
using total-degree start systems, multihomogeneous-degree
start systems, and also user defined homotopies.
- Implements parameter
continuation for families of systems, such as the inverse kinematics of
six-revolute serial-link arms, or the forward kinematics of Stewart-Gough
- Adaptive multiprecision implemented for finding isolated
solutions and for the numerical irreducible decomposition.
positive-dimensional solutions by computing witness sets.
- Has automatic
differentiation which preserves the straightline
quality of an input system.
- Uses homogenization to
accurately compute solutions "at infinity."
- Provides a fractional
power-series endgame to accurately compute singular roots
- Allows for subfunctions.
- Allows for witness set
manipulation via both sampling and membership testing.
- Accepts square or nonsquare systems.
Bertini and the material in the Bertini website are based upon work supported partially by
the National Science Foundation under Grants DMS - 041007 and DMS - 0712910.
Any opinions, findings, and conclusions or recommendations expressed in this
material are those of the authors and do not necessarily reflect the views of
the National Science Foundation.
Andrew J. Sommese/ firstname.lastname@example.org /revised December