ALGORITHM FOR COMPUTING THE TRUNCATION OF THE DISCRIMINANT OF A POLINOMIAL

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Resumo

A program that computes the truncation of the discriminant for a polynomial of one variable onto facets of the Newton polytope for the discriminant of this polynomial, as well as enables the factorization of this truncation into the product of discriminants of polynomials of lower degrees, is developed.

Sobre autores

A. LYAPIN

Siberian Federal University; Fairmont State University

Email: aplyapin@sfu-kras.ru
Krasnoyarsk, Russia; Fairmont, WV 26554, USA

E. MIKHALKIN

Siberian Federal University

Autor responsável pela correspondência
Email: mikhalkin@bk.ru
Krasnoyarsk, Russia

Bibliografia

  1. Gelfand I., Kapranov M., Zelevinsky A. Discriminants, resultants and multidimensional determinants. Birkhäuser: Boston, 1994.
  2. Васильев В.А. Ветвящиеся интегралы. М.: МЦНМО, 2000.
  3. Antipova I.A., Kleshkova E.A. On Facets Of The Newton Polytope For The Discriminant Of The Polynomial System // Siberian Electronic Mathematical Reports. 2021. V. 18 (2.1). P. 1180–1188.
  4. Ardila F. The Geometry of Matroids // Notices Amer. Math. Soc. 2018. V. 65 (8). P. 902–908.
  5. Dickenstein A., Feichtner E.M., Sturmfels B. Tropical discriminants // J. Amer. Math. Soc. 2007. V. 20. P. 1111–1133.
  6. Krasikov V.A., Sadykov T.M. On the analytic complexity of discriminants // Proceedings of the Steklov Institute of Mathematics. 2012. V. 279. P. 78–92.
  7. Михалкин Е.Н., Степаненко В.А., Цих А.К. Геометрия факторизационных тождеств для дискриминантов // Доклады Российской академии наук. Серия: математика, информатика, процессы управления. 2020. Т. 493. С. 21–25.
  8. Mikhalkin E.N., Stepanenko V.A., Tsikh A.K. Blow-ups for the Horn-Kapranov parametrization of the classical discriminant. B кн. “Partial Differential Equations, Spectral Theory, and Mathematical Physics”. EMS Series of Congress Reports. Publication house EMS. 2021. P. 315–329.
  9. Mikhalkin E.N., Nikzad M., Stepanenko V.A. Detailed Factorization Identiies for Classical Discriminant // Journal of Siberian Federal University. Mathematics & Physics. 2022. V. 15 (1.1). P. 23–28.
  10. Passare M., Tsikh A. Algebraic equations and hypergeometric series. In the book “The legacy of Niels Henrik Abel”. Springer: Berlin-Heidelberg-New York, 2004. P. 653–672.

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Declaração de direitos autorais © А.П. Ляпин, Е.Н. Михалкин, 2023

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