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Finding vacua for the four dimensional effective theories for supergravity which descend from flux compactifications and analyzing them according to their stability is one of the central problems in string phenomenology.
Finding all isolated solutions to polynomial systems using hompack
Sommese-A J Morgan, A P and Layne T. Watson · 1989
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The magma algebra system i: the user language
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Algorithm 795: Phcpack: a general-purpose solver for polynomial systems by homotopy continuation
Jan Verschelde · 1999
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Energy landscape of a lennard-jones liquid: Statistics of stationary points
Kurt Broderix, Kamal K. Bhattacharya, Andrea Cavagna, Annette Zippelius, and Irene Giardina · 2000
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Saddle points and dynamics of Lennard-Jones clusters, solids, and supercooled liquids
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A new efficient algorithm for computing gröbner bases without reduction to zero (f5)
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Geometric Approach to the Dynamic Glass Transition
T. S. Grigera, A. Cavagna, I. Giardina, and G. Parisi · 2002
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Solving polynomial systems by the homotopy continuation method
T Y Li · 2003
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Stationary points and dynamics in high-dimensional systems
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Phom: a polyhedral homotopy continuation method for polynomial systems
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Energy Landscapes : Applications to Clusters, Biomolecules and Glasses (Cambridge Molecular Science)
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Algorithm 846: Mixedvol: a software package for mixed-volume computation
Tangan Gao, T. Y. Li, and Mengnien Wu · 2005
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Involutive Algorithms for Computing Groebner Bases
V. P. Gerdt · 2005
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The numerical solution of systems of polynomials arising in Engineering and Science
Andrew J Sommese and Charles W Wampler · 2005
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Algorithmic algebraic geometry and flux vacua
James Gray, Yang-Hui He, and Andre Lukas · 2006
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M-theory on seven-dimensional manifolds with SU(3) structure
Andrei Micu, Eran Palti, and P.M. Saffin · 2006
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Lattice Landau gauge via Stereographic Projection
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A Simple Introduction to Grobner Basis Methods in String Phenomenology
James Gray · 2009
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STRINGVACUA: A Mathematica Package for Studying Vacuum Configurations in String Phenomenology
James Gray, Yang-Hui He, Anton Ilderton, and Andre Lukas · 2009
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Lattice Landau Gauge and Algebraic Geometry
D. B. Mehta, A. Sternbeck, L. von Smekal, and A. G. Williams · 2009
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Lattice vs. Continuum: Landau Gauge Fixing and ’t Hooft-Polyakov Monopoles
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alphaCertified: certifying solutions to polynomial systems
J. D. Hauenstein and F. Sottile · 2010
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Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)
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A New Method for Finding Vacua in String Phenomenology
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Modified Lattice Landau Gauge
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Hom4ps-2.0, a software package for solving polynomial systems by the polyhedral homotopy continuation method
T L Lee, T Y Li, and C H Tsai · 2008
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Available at http://www.nd.edu/ ∼ \sim sommese/bertini
Daniel J. Bates, Jonathan D. Hauenstein, Andrew J. Sommese, and Charles W. Wampler
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Macaulay2, a software system for research in algebraic geometry
Daniel R. Grayson and Michael E. Stillman
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Singular
G.-M.; Pfister G.; Schönemann H. Decker, W.; Greuel · 2011
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Stationary point analysis of the one-dimensional lattice landau gauge fixing functional, aka random phase xy hamiltonian
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