Journal of the Korean Society for Industrial and Applied Mathematics

  • 제27권1호
  • /
  • Pages.1-22
  • /
  • 2023
  • /
  • 1226-9433(pISSN)
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  • 1229-0645(eISSN)
한국산업응용수학회 (Korean Society for Industrial and Applied Mathematics)
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A FAMILY OF EXPLICIT WARING DECOMPOSITIONS OF A POLYNOMIAL

  • KANGJIN HAN (SCHOOL OF UNDERGRADUATE STUDIES, DAEGU-GYEONGBUK INSTITUTE OF SCIENCE & TECHNOLOGY (DGIST)) ;
  • HYUNSUK MOON (SCHOOL OF MATHEMATICS, KOREA INSTITUTE FOR ADVANCED STUDY (KIAS))
  • 투고 : 2022.12.14
  • 심사 : 2023.02.27
  • 발행 : 2023.03.25
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초록

In this paper we settle some polynomial identity which provides a family of explicit Waring decompositions of any monomial Xa00 Xa11··· Xann over a field k. This gives an upper bound for the Waring rank of a given monomial and naturally leads to an explicit Waring decomposition of any homogeneous form and, eventually, of any polynomial via (de)homogenization. Note that such decomposition is very useful in many applications dealing with polynomial computations, symmetric tensor problems and so on. We discuss some computational aspect of our result as comparing with other known methods and also present a computer implementation for potential use in the end.

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과제정보

The first author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2021R1F1A104818611) and the second author was supported by KIAS Individual Grant (MG083101) at Korea Institute of Advanced Study (KIAS).

참고문헌

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