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TMF, 2010, Volume 163, Number 2, Pages 222–257 (Mi tmf6497)  

This article is cited in 12 scientific papers (total in 12 papers)

New and old results in resultant theory

A. Yu. Morozova, Sh. R. Shakirovab

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

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

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

Full text: PDF file (713 kB)
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English version:
Theoretical and Mathematical Physics, 2010, 163:2, 587–617

Bibliographic databases:

Received: 16.11.2009

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

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Kazuyuki Fujii, “Beyond the Gaussian”, SIGMA, 7 (2011), 022, 12 pp.  mathnet  crossref  mathscinet
    2. Hu Sh., Huang Zh.-H., Ling Ch., Qi L., “On Determinants and Eigenvalue Theory of Tensors”, J. Symbolic Comput., 50 (2013), 508–531  crossref  mathscinet  zmath  isi  elib  scopus
    3. Lasserre J.B., “Recovering an Homogeneous Polynomial From Moments of its Level Set”, Discret. Comput. Geom., 50:3 (2013), 673–678  crossref  mathscinet  zmath  isi  elib  scopus
    4. Semenyakin M., “On Diagrammatic Technique For Nonlinear Dynamical Systems”, Mod. Phys. Lett. A, 29:35 (2014), 1430039  crossref  mathscinet  zmath  adsnasa  isi  scopus
    5. A. V. Seliverstov, “Kubicheskie formy bez monomov ot dvukh peremennykh”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 25:1 (2015), 71–77  mathnet  elib
    6. Kononov Ya. Morozov A., “Colored Homfly and Generalized Mandelbrot Set”, J. High Energy Phys., 2015, no. 11, 151  crossref  mathscinet  zmath  isi  elib  scopus
    7. Lasserre J.B., “a Generalization of Lowner-John'S Ellipsoid Theorem”, Math. Program., 152:1-2 (2015), 559–591  crossref  mathscinet  zmath  isi  elib  scopus
    8. Lasserre J.B., “Convex Optimization and Parsimony of $L_p$-balls Representation”, SIAM J. Optim., 26:1 (2016), 247–273  crossref  mathscinet  zmath  isi  elib  scopus
    9. Kytmanov A.M., Naprienko Ya.M., “An approach to define the resultant of two entire functions”, Complex Var. Elliptic Equ., 62:2 (2017), 269–286  crossref  mathscinet  zmath  isi  elib  scopus
    10. Itoyama H. Mironov A. Morozov A., “Ward Identities and Combinatorics of Rainbow Tensor Models”, J. High Energy Phys., 2017, no. 6, 115  crossref  mathscinet  zmath  isi  scopus
    11. Olga V. Khodos, “An approach to determine the resultant of two entire functions”, Zhurn. SFU. Ser. Matem. i fiz., 11:2 (2018), 264–268  mathnet  crossref
    12. A. M. Kytmanov, O. V. Khodos, “An approach to the determination of the resultant of two entire functions”, Russian Math. (Iz. VUZ), 62:4 (2018), 42–51  mathnet  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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