Sample Bertini interfaces

Bertini is a software package for computation in numerical algebraic geometry under ongoing development by D. Bates, J. Hauenstein, A. Sommese, and C. Wampler. If you want to know more about Bertini, please follow the link above.

Bertini is a useful computational tool, but the file-based input/output format can seem imposing to new users. The structure of the input and output files is fairly straightforward (as described in the user's manual), but Bertini would be much easier to use if there were interfaces to common software packages such as Maple, Matlab, or one of the several standard algebraic geometry packages (Singular, Macaulay, CoCoA, etc.).

The point of this webpage is to briefly describe how to interact with Bertini from within these packages. Full interfaces would of course be preferrable, and they are in fact on the Bertini development plan. Until those full interfaces are available, though, hopefully the ideas on this webpage will help you get started with using Bertini as a computational engine.

If you have questions, please feel free to contact me. Also, if you choose to extend the files below to be more sophisticated or more general, I would be delighted to here about and perhaps even post your work!

Matlab interface

This sample interface is very specific to a problem that I worked on in optimal control. However, I have added numerous comments to the files below (and removed some of the non-interface content) to help interested Bertini users understand how to interact with Bertini.

If you are looking to solve one polynomial system at a time (i.e., not parameterized families of systems), then you should check out the following m-file:

m-file for automatic homotopies

This file will write a polynomial system into this input file, call Bertini, read in the finite solutions contained in this output file, and finally create this "start" file to be used below (in the case of parameterized families of systems).

If, on the other hand, you are looking to solve parameterized systems, you should start with the file above (for one solve at a random complex point in the parameter space) and then look at the following file (for repeated solves at user-specified points in the parameter space):

m-file for parameter homotopies

This file will write a complete homotopy (containing the target polynomial system) to this input file, call Bertini (using the start file from above), and finally read in the real solutions contained in this output file.

Maple interface

Although I have interacted with Bertini from within Maple for several projects now, I have not yet had the time to prepare any of those samples for public consumption. I will post it here as soon as I have done so. Please bug me about this if you would like to use this interface!

Other interfaces

Interfaces to other packages are planned, but little progress has been made as of 10/19/07. Again, please bug me if this would be of interest to you. Development of such interfaces could take a bit more time, but significant interest from potential users would certainly effect the order of the development plan.

Page maintained by Dan Bates.

Last updated on October 19, 2007.