Numerically Computing Galois Groups: Computations and Software

Information

Click the link here to download a zip file containing folders to run examples from Numerically Computing Galois Groups.

To perform the computations one needs to have the numerical algebraic geometry software Bertini and the Macaulay2 package Bertini.m2.

Once the Macaulay2 package Bertini.m2 has been installed one can see examples entering: "viewHelp b'PHGaloisGroup" or "help b'PHGaloisGroup".

After unpacking the zip file "GGExamples", we create a directory to refer to a particular folder. For example:

theDir="/Users/Tamir/Desktop/GGExamples/cubicSurfaceExFiles"

The directory, theDir, contains preprocessed files:

1. input file to determine critical points,

2. critical points,

3. branch points,

4. input file to determine the Galois group.

5. start parameter file that gives a point in C_t^1.

6. start solution file that gives a general fiber,

7. generators of the Galois group,

8. M2 file that has code to recreate files 1-7.