The Babylonian quest to solve polynomial equations ushered in monodromy and geometric perceptions of how objects exhibit singularity behaviors. The real-world application of braid monodromy is more complicated than other permutation groups. How should braid monodromy be applied to compute the invariables of exteriors and curvatures in objects like airplanes? Aktas and Akbas present efficient algorithms for computing the braid monodromy of an entirely transformable n-gonal curvature and the Alexander multinomial of such curvature supplements.

The paper uses a rectangular braid diagram (RBD) to create a precise, totally shrinkable n-gonal curvature. The diagram is then used to “obtain the loops around its singular fibers and compute the braid monodromy on each loop using an adaptive step size method.” Libgober’s reputable theorem of invariants in algebraic geometry [1] is used in conjunction with RBD to create an effective algorithm for computing the Alexander multinomial of fully reductive n-gonal curvatures.

The authors present clear examples and illustrations for the Burau braid groups, RBD, braid monodromy, and Alexander multinomial computation. The efficiencies of the computing algorithms compare favorably with the braid monodromy experimental results in the literature. The paper is for all algorithmic designers and analysts.