Bertini Home Page
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 continuation.
- Authors: Daniel
J. Bates, Jonathan 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.
Key Features:
- 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 parallel-link robots.
- Adaptive multiprecision
implemented for finding isolated solutions and for the numerical
irreducible decomposition.
- Treats 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 Links
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.
Alexandra
Seremina has kindly made <a href="http://www.azoft.com/people/seremina/edu/bertini-rom.html">this
page available in Romanian</a> courtesy of <a href="http://www.azoft.com/">azoft</a>
Maintained by
Andrew J. Sommese/ sommese@nd.edu /revised May 21, 2010