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
- License Policy
- Download Page
- Documentation on installation and use.
- Please write to one of us (email addresses on webpages linked to above) to report bugs or tell us what you like/dislike about Bertini.
If you use Bertini in a publication, we would love to hear about it!- Example 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.
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since
October 24, 2006.
Maintained by Andrew J. Sommese/ sommese@nd.edu /revised April 20, 2008