A. Yu. Morozov, Sh. R. Shakirov, “New and old results in resultant theory”, TMF, 163:2 (2010), 222–257; Theoret. and Math. Phys., 163:2 (2010), 587

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Teoreticheskaya i Matematicheskaya Fizika, 2010, Volume 163, Number 2, Pages 222–257
DOI: https://doi.org/10.4213/tmf6497 (Mi tmf6497)

This article is cited in 37 scientific papers (total in 37 papers)

New and old results in resultant theory

A. Yu. Morozov^a, Sh. R. Shakirov^ab

^a Institute for Theoretical and Experimental Physics. Moscow, Russia
^b Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Oblast, Russia

Full-text PDF (713 kB) Citations (37)

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DOI: https://doi.org/10.4213/tmf6497

Abstract: Resultants play an increasingly important role in modern theoretical physics: they appear whenever we have nonlinear (polynomial) equations, nonquadratic forms, or non-Gaussian integrals. Being a research subject for more than three hundred years, resultants are already quite well studied, and many explicit formulas, interesting properties, and unexpected relations are known. We present a brief overview of these results, from classical ones to those obtained relatively recently. We emphasize explicit formulas that could bring practical benefit in future physical research.

Keywords: resultant, discriminant, non-Gaussian integral, nonlinear algebra.

Received: 16.11.2009

English version:
Theoretical and Mathematical Physics, 2010, Volume 163, Issue 2, Pages 587–617
DOI: https://doi.org/10.1007/s11232-010-0044-0

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: A. Yu. Morozov, Sh. R. Shakirov, “New and old results in resultant theory”, TMF, 163:2 (2010), 222–257; Theoret. and Math. Phys., 163:2 (2010), 587–617

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https://www.mathnet.ru/eng/tmf6497

https://doi.org/10.4213/tmf6497

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This publication is cited in the following 37 articles:

Xun Shen, Ye Wang, Kazumune Hashimoto, Yuhu Wu, Sebastien Gros, “Probabilistic reachable sets of stochastic nonlinear systems with contextual uncertainties”, Automatica, 176 (2025), 112237
V. I. Kuzovatov, A. A. Kytmanov, “On the Calculation of the Number of Real Roots of a System of Nonalgebraic Equations Using Computer Algebra”, Program Comput Soft, 51:2 (2025), 83
Yaroslav Drachov, “Generalized $\widetilde{W}$ algebras”, Eur. Phys. J. C, 84:10 (2024)
V. V. Dolotin, A. Yu. Morozov, A. V. Popolitov, “Machine learning of the well-known things”, Theoret. and Math. Phys., 214:3 (2023), 446–455
Vyacheslav I. Kuzovatov, Evgeniya K. Myshkina, Anastasia S. Bushkova, “On an approach to finding sums of multiple numerical series”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 46 (2023), 85–97
V. Mishnyakov, A. Morozov, P. Suprun, “Position space equations for banana Feynman diagrams”, Nuclear Physics B, 992 (2023), 116245
Khazhgali Kozhasov, Jean B. Lasserre, “Volumes of Sublevel Sets of Nonnegative Forms and Complete Monotonicity”, SIAM J. Appl. Algebra Geometry, 7:4 (2023), 768
Yifan Liu, Jiazhi Cai, Lei Hou, Bo Yan, Liqun Chen, Qingbin Gao, “Bistable dynamics analysis using Padé approximation and resultant theory”, International Journal of Non-Linear Mechanics, 149 (2023), 104325
Evgeniya K. Myshkina, “On a formula for calculating the resultant of two entire functions”, Zhurn. SFU. Ser. Matem. i fiz., 15:1 (2022), 17–22
Patil G.U., Matlack K.H., “Review of Exploiting Nonlinearity in Phononic Materials to Enable Nonlinear Wave Responses”, Acta Mech., 233:1 (2022), 1–46
Kuzovatov I V., Kytmanov A.A., Myshkina E.K., “On Computing the Resultant of a Polynomial and An Entire Function”, Program. Comput. Softw., 48:1 (2022), 59–64
Loi Le Ta, Minh Quy Pham, “BOUNDS FOR VOLUMES OF SUB-LEVEL SETS OF POLYNOMIALS AND APPLICATIONS”, DLU JOS, 2022, 26
Frédéric Holweck, Luke Oeding, “Hyperdeterminants from the E8 discriminant”, Journal of Algebra, 593 (2022), 622
Kuzovatov I V., Kytmanov A.A., Myshkina E.K., “An Algorithm For Constructing the Resultant of Two Entire Functions”, Program. Comput. Softw., 47:2 (2021), 139–143
Zheng Ya.-N., “The Characteristic Polynomial of the Complete 3-Uniform Hypergraph”, Linear Alg. Appl., 627 (2021), 275–286
Matrix and Tensor Decompositions in Signal Processing, 2021, 329
A. M. Kytmanov, E. K. Myshkina, “On finding the resultant of two entire functions”, Probl. anal. Issues Anal., 9(27):3 (2020), 119–130
Hvatov A., Sorokin S., “Analysis of Periodicity-Induced Attenuation Effect in a Nonlinear Waveguide By Means of the Method of Polynomial System Resultants”, Mech. Res. Commun., 103 (2020), UNSP 103476
Bao Ya.-H. Fan Y.-Zh. Wang Y. Zhu M., “A Combinatorial Method For Computing Characteristic Polynomials of Starlike Hypergraphs”, J. Algebr. Comb., 51:4 (2020), 589–616
A. Yu. Morozov, “Cut-and-join operators and Macdonald polynomials from the 3-Schur functions”, Theoret. and Math. Phys., 200:1 (2019), 938–965

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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