Interfaces the functionality of the software Bertini to solve polynomial systems and perform calculations in numerical algebraic geometry. The software is available at http://bertini.nd.edu/. Bertini is under ongoing development by D. Bates, J. Hauenstein, A. Sommese, and C. Wampler.
The user may place the executable program bertini in the executation path. Alternatively, the path to the executable needs to be specified, for instance,
i1 : needsPackage("Bertini", Configuration=>{"BERTINIexecutable"=>"/folder/subfolder/bertini"}) o1 = Bertini o1 : Package |
Below is a simple example using the most popular function, a basic zero-dimensional solve with no special options.
i2 : R = CC[x,y] o2 = R o2 : PolynomialRing |
i3 : F = {x^2-1,y^2-1} 2 2 o3 = {x - 1, y - 1} o3 : List |
i4 : solns = bertiniZeroDimSolve(F) ~/bertini o4 = {{1, 1}, {1, -1}, {-1, 1}, {-1, -1}} o4 : List |