New and old results in resultant theory
New and old results in resultant theory
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DOI：
10.1007/s11232-010-0044-0
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发表时间：
2009-11
影响因子：
1
通讯作者：
Алексей Юрьевич Морозов;A. Morozov;Шамиль Ринатович Шакиров;Shamil Shakirov
中科院分区：
文献类型：
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作者：
Алексей Юрьевич Морозов;A. Morozov;Шамиль Ринатович Шакиров;Shamil Shakirov
结果在现代理论物理中扮演着越来越重要的角色：每当我们有非线性(多项式)方程、非二次形式或非高斯积分时，它们就会出现。作为一个研究了三百多年的课题，结式的研究已经相当深入，许多显式、有趣的性质和意想不到的关系都已为人所知。我们给出了这些结果的简要概述，从经典结果到最近获得的结果。我们强调明确的公式，可以在未来的物理研究中带来实际的好处。
Resultants play an increasingly important role in modern theoretical physics: they appear whenever we have nonlinear (polynomial) equations, nonquadratic forms, or non-Gaussian integrals. Being a research subject for more than three hundred years, resultants are already quite well studied, and many explicit formulas, interesting properties, and unexpected relations are known. We present a brief overview of these results, from classical ones to those obtained relatively recently. We emphasize explicit formulas that could bring practical benefit in future physical research.