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COMPUTATIONAL ASPECTS OF THE HORN–KAPRANOV PARAMETRIZATION
- Authors: Sadykov T.M.1
-
Affiliations:
- Plekhanov Russian University of Economics
- Issue: No 2 (2025)
- Pages: 64-72
- Section: COMPUTER ALGEBRA
- URL: https://journals.rcsi.science/0132-3474/article/view/292084
- DOI: https://doi.org/10.31857/S0132347425020083
- EDN: https://elibrary.ru/DISCRC
- ID: 292084
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Abstract
This paper presents algorithms for computing the Horn–Kapranov uniformization of some discriminant varieties and discusses the performance of the software implementation of these algorithms in the Mathematica computer algebra system.
About the authors
T. M. Sadykov
Plekhanov Russian University of Economics
Email: Sadykov.TM@rea.ru
Moscow, Russia
References
- Gelfand I.M., Kapranov M.M., Zelevinsky A.V. Discriminants, Resultants, Multidimensional Determinants. Birkhauser 1994.
- Krasikov V.A., Sadykov T.M. On the analytic complexity of discriminants // Proceedings of the Steklov Institute of Mathematics. 2012. No. 279:1. P. 78–92.
- Huggins P., Sturmfels B., Yu J., Yuster D.S. The hyperdeterminant and triangulations of the 4cube // Mathematics of Computation. 2008. No. 77. P. 1653–1679.
- Horn J. Uber die Konvergenz der hypergeometrischen Reihen zweier und dreier Veranderlichen // Mathematische Annalen. 1889. No. 34. P. 544–600.
- Kapranov M.M. A characterization of A-discriminantal hypersurfaces in terms of the logarithmic Gauss map // Mathematische Annalen. 1991. No. 290:1. P. 277–285.
- Forsgard J. Defective dual varieties for real spectra // Journal of Algebraic Combinatorics. 2019. No. 49. P. 49–67.
- Forsgard J., deWolff T. The algebraic boundary of the SONCcone // SIAM Journal on Applied Algebra and Geometry. 2022. No. 6:3. P. 468–502.
- Filiz I.O., Guo X., Morton J., Sturmfels B. Graphical models for correlated defaults // Mathematical Finance. 2012. No. 22:4. P. 621–644.
- Duarte E., Marigliano O., Sturmfels B. Discrete statistical models with rational maximum likelihood estimator // Bernoulli. 2021. No. 27:1. P. 135–154.
- Amendola C., Bliss N., Burke I., Gibbons C.R., Helmer M., Hosten S., Nash E.D., Rodriguez J.I., Smolkin D. The maximum likelihood degree of toric varieties // Journal of Symbolic Computation. 2019. No. 92. P. 222–242.
- Catanese F., Hosten S., Khetan A., Sturmfels B. The maximum likelihood degree // American Journal of Mathematics. 2006. No. 128:3. P. 671–697.
- Emiris I.Z., Karasoulou A. Sparse discriminants and applications // Springer Proceedings in Mathematics and Statistics. 2014. No. 84. P. 55–71.
- Mikhalkin E.N., Tsikh A.K. Singular strata of cuspidal type for the classical discriminant // Sbornik Mathematics. 2015. No. 206. P. 282–310.
- Tanabe S. On Horn–Kapranov uniformisation of the discriminantal loci // Adv. Stud. Pure Math.
- Singularities in Geometry and Topology. 2004. No. 46. P. 223–249.
- Cueto M.A., Dickenstein A. Some results on inhomogeneous discriminants // Proceedings of the XVI Coloquio Latinoamericano de Algebra. Biblioteca de la Revista Matematica Iberoamericana, Colonia del Sacramento. Uruguay. P. 42–61.
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