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- 한국산업응용수학회 JOURNAL OF THE KOREAN SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS Journal of the Korean Society for Industrial and Applied Mathematics Vol.27 No.1
- 발행연도
- 2023.3
- 수록면
- 1 - 22 (22page)
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In this paper we settle some polynomial identity which provides a family of explicit Waring decompositions of any monomial X<SUP>a₀</SUP>₀ X<SUP>a₁</SUP>₁· · ·X<SUP>an</SUP>n 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.
목차
ABSTRACT
1. INTRODUCTION
2. MAIN RESULT
3. CASE OF ARBITRARY HOMOGENEOUS FORM
4. MACAULAY2 CODE FOR THE DECOMPOSITIONS
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UCI(KEPA) : I410-ECN-0101-2023-410-001333739