Category:Package bertini

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The basic idea behind this package is to make Bertini usable in/with ApCoCoA. Bertini uses Homotopy Continuation Method for Polynomial System Solving.

Please note: The function(s) explained on this page is/are using the ApCoCoAServer. You will have to start the ApCoCoAServer in order to use it/them.

The bertini.exe must be in the ApCoCoA directory/Bertini and you must have the permissions to read and write in this directory.


Numerical algebraic geometry is the study based on homotopy continuation method and algebraic geometry. It has same relation to algebraic geomertry, as Numerical Linear Algebra to linear algebra. In Numerical Algebraic Geometry we can fine isolated solutions. For positive dimensional systems, we can find out numerical irreducible deocmpostions.

Bertini: Software for Numerical Algebraic Geometry

Bertini is a software desgined for computations in Numerical Algebric Geometry, particularly, for solving polynomial systems numerically using homotopy continuation method available at [1]. Its a general-purpose solver, written in C, that was created for research about polynomial continuation.

The Key Features of Bertini are:

  • 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 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.