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hyperplane arrangement algorithm and complexity

Hi there, I wonder what kind of the algorithm the hyperplane arrangement algorithm is using and what's the complexity with regarding to the number of hyperplanes. Specifically, the bounded_region method. Suppose we are in d-dimension with n hyperplanes. I check the source code and can only find " This module implements hyperplane arrangements defined over the rationals or over finite fields. The original motivation was to make a companion to Richard Stanley's notes [Sta2007]_ on hyperplane arrangements." Thanks so much for your time and help!