Standard

Waring problem as an issue of polynomial computer algebra. / Vavilov, Nikolai .

International Conference Polynomial Computer Algebra 2020: St Petersburg October 2020. ed. / Николай Васильев. Международный математический институт им. Эйлера, 2020.

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearchpeer-review

Harvard

Vavilov, N 2020, Waring problem as an issue of polynomial computer algebra. in Н Васильев (ed.), International Conference Polynomial Computer Algebra 2020: St Petersburg October 2020. Международный математический институт им. Эйлера, Polynomial Computer Algebra '2020, St. Petersburg, Russian Federation, 12/10/20.

APA

Vavilov, N. (Accepted/In press). Waring problem as an issue of polynomial computer algebra. In Н. Васильев (Ed.), International Conference Polynomial Computer Algebra 2020: St Petersburg October 2020 Международный математический институт им. Эйлера.

Vancouver

Vavilov N. Waring problem as an issue of polynomial computer algebra. In Васильев Н, editor, International Conference Polynomial Computer Algebra 2020: St Petersburg October 2020. Международный математический институт им. Эйлера. 2020

Author

Vavilov, Nikolai . / Waring problem as an issue of polynomial computer algebra. International Conference Polynomial Computer Algebra 2020: St Petersburg October 2020. editor / Николай Васильев. Международный математический институт им. Эйлера, 2020.

BibTeX

@inproceedings{ecafbdb950f84eddaf14ae5cbeb72e74,
title = "Waring problem as an issue of polynomial computer algebra",
abstract = "In its original XVIII century form the classical Waring problem consisted in finding for each natural $k$ the smallest such $s=g(k)$ that all natural numbers $n$ can be written as sums of $s$ non-negative $k$-th powers, $n=x_1^k+\ldots+x_s^k$. In the XIX century the problem was modified as the quest of finding such minimal $s=G(k)$ that {\it almost all\/} $n$ can be expressed in this form. In the XX century this problem was further specified, as for finding such $G(k)$ {\it and\/} the precise list of exceptions. In the present talk I sketch the key steps in the solution of this problem, with a special emphasis on algebraic and computational aspects. I describe various connections of this problem, and its modifications, such as the rational Waring problem, the easier Waring problem, etc., with the current research in polynomial computer algebra,especially with identities, symbolic polynomials, etc. and promote several outstanding computational challenges. ",
keywords = "Waring problem, easier Waring problem, rational Waring problem, polynomial identities, sums of cubes, sums of biquadrates",
author = "Nikolai Vavilov",
year = "2020",
month = oct,
day = "4",
language = "English",
editor = "Николай Васильев",
booktitle = "International Conference Polynomial Computer Algebra 2020",
publisher = "Международный математический институт им. Эйлера",
address = "Russian Federation",
note = "Polynomial Computer Algebra '2020, PCA 2020 ; Conference date: 12-10-2020 Through 17-10-2020",
url = "https://pca-pdmi.ru/2020/",

}

RIS

TY - GEN

T1 - Waring problem as an issue of polynomial computer algebra

AU - Vavilov, Nikolai

PY - 2020/10/4

Y1 - 2020/10/4

N2 - In its original XVIII century form the classical Waring problem consisted in finding for each natural $k$ the smallest such $s=g(k)$ that all natural numbers $n$ can be written as sums of $s$ non-negative $k$-th powers, $n=x_1^k+\ldots+x_s^k$. In the XIX century the problem was modified as the quest of finding such minimal $s=G(k)$ that {\it almost all\/} $n$ can be expressed in this form. In the XX century this problem was further specified, as for finding such $G(k)$ {\it and\/} the precise list of exceptions. In the present talk I sketch the key steps in the solution of this problem, with a special emphasis on algebraic and computational aspects. I describe various connections of this problem, and its modifications, such as the rational Waring problem, the easier Waring problem, etc., with the current research in polynomial computer algebra,especially with identities, symbolic polynomials, etc. and promote several outstanding computational challenges.

AB - In its original XVIII century form the classical Waring problem consisted in finding for each natural $k$ the smallest such $s=g(k)$ that all natural numbers $n$ can be written as sums of $s$ non-negative $k$-th powers, $n=x_1^k+\ldots+x_s^k$. In the XIX century the problem was modified as the quest of finding such minimal $s=G(k)$ that {\it almost all\/} $n$ can be expressed in this form. In the XX century this problem was further specified, as for finding such $G(k)$ {\it and\/} the precise list of exceptions. In the present talk I sketch the key steps in the solution of this problem, with a special emphasis on algebraic and computational aspects. I describe various connections of this problem, and its modifications, such as the rational Waring problem, the easier Waring problem, etc., with the current research in polynomial computer algebra,especially with identities, symbolic polynomials, etc. and promote several outstanding computational challenges.

KW - Waring problem

KW - easier Waring problem

KW - rational Waring problem

KW - polynomial identities

KW - sums of cubes

KW - sums of biquadrates

UR - https://pca-pdmi.ru/2020/files/53/Vavilov-PCA2020_new.pdf

M3 - Conference contribution

BT - International Conference Polynomial Computer Algebra 2020

A2 - Васильев, Николай

PB - Международный математический институт им. Эйлера

T2 - Polynomial Computer Algebra '2020

Y2 - 12 October 2020 through 17 October 2020

ER -

ID: 62862477