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Bernstein–Khovanskii–Kushnirenko theorem : ウィキペディア英語版 | Bernstein–Kushnirenko theorem Bernstein–Kushnirenko theorem (also known as BKK theorem or Bernstein–Khovanskii–Kushnirenko theorem 〔 *David A. Cox; J. Little; D. O'Shea Using algebraic geometry. Second edition. Graduate Texts in Mathematics, 185. Springer, 2005. xii+572 pp. ISBN 0-387-20706-6〕), proven by David Bernstein 〔D. N. Bernstein, "The number of roots of a system of equations", ''Funct. Anal. Appl.'' 9 (1975), 183–185〕 and Anatoli Kushnirenko 〔A. G. Kouchnirenko, "Polyhedres de Newton et nombres de Milnor", ''Invent. Math.'' 32 (1976), 1–31〕 in 1975, is a theorem in algebra. It claims that the number of non-zero complex solutions of a system of Laurent polynomial equations ''f''1 = 0, ..., ''f''''n'' = 0 is equal to the mixed volume of the Newton polytopes of ''f''1, ..., ''f''''n'', assuming that all non-zero coefficients of ''fn'' are generic. More precise statement is as follows: ==Theorem statement==
Let be a finite subset of . Consider the subspace of the Laurent polynomial algebra 抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)』 ■ウィキペディアで「Bernstein–Kushnirenko theorem」の詳細全文を読む
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