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The problem of solving a system of polynomial equations is one of the mostfundamental problems in applied mathematics. Among them, the problem of solvinga system of binomial equations form a important subclass for which specializedtechniques exist. For both theoretic and applied purposes, the degree of thesolution set of a system of binomial equations often plays an important role inunderstanding the geometric structure of the solution set. Its computation,however, is computationally intensive. This paper proposes a specializedparallel algorithm for computing the degree on GPUs that takes advantage of themassively parallel nature of GPU devices. The preliminary implementation showsremarkable efficiency and scalability when compared to the closest CPU-basedcounterpart. Applied to the "master space problem of $\mathcal{N}=1$ gaugetheories" the GPU-based implementation achieves nearly 30 fold speedup over itsCPU-only counterpart enabling the discovery of previously unknown results.Equally important to note is the far superior scalability: with merely 3 GPUdevices on a single workstation, the GPU-based implementation shows betterperformance, on certain problems, than a small cluster totaling 100 CPU cores.

Parallel degree computation for solution space of binomial systems with an application to the master space of $\mathcal{N}=1$ gauge theories