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New and old results in resultant theory

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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.

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Authors and Affiliations

  1. Institute for Theoretical and Experimental Physics, Moscow, Russia

    A. Yu. Morozov & Sh. R. Shakirov

  2. Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Oblast, Russia

    Sh. R. Shakirov

Authors
  1. A. Yu. Morozov
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  2. Sh. R. Shakirov
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Correspondence to A. Yu. Morozov.

Additional information

To simplify our considerations in this paper, we assume that the polynomial equations are homogeneous. In fact, the homogeneity condition is inessential, and the entire theory expounded here can also be formulated for inhomogeneous polynomials.

Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 163, No. 2, pp. 222–257, May, 2010.

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Morozov, A.Y., Shakirov, S.R. New and old results in resultant theory. Theor Math Phys 163, 587–617 (2010). https://doi.org/10.1007/s11232-010-0044-0

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