2013/01/05 by Yang‐Hui He, Dhagash Mehta, He, Yang-Hui +7
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Numerical Analysis Techniques #Artificial intelligence #Black Holes and Theoretical Physics #Compactification (mathematics) #Computer science #FOS: Mathematics #FOS: Physical sciences #Gravitino #High Energy Physics - Theory (hep-th) #Homotopy #Mathematical physics #Mathematics #Moduli space #Numerical Analysis (math.NA) #Physics #Polynomial and algebraic computation #Pure mathematics #Statistical Mechanics (cond-mat.stat-mech) #Supergravity #Supersymmetry #Theoretical computer science #Theoretical physics #Variety (cybernetics)
paper · pdf · doi:10.48550/arxiv.1301.0946
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2013/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Solving large polynomial systems with coefficient parameters are ubiquitous and constitute an important class of problems. We demonstrate the computational power of two methods--a symbolic one called the Comprehensive Gröbner basis and a numerical one called the cheater's homotopy-applied to studying both potential energy landscapes and a variety of questions arising from geometry and phenomenology. Particular attention is paid to an example in flux compactification where important physical quantities such as the gravitino and moduli masses and the string coupling can be efficiently extracted.