منابع مشابه
Galois Groups of Cubics and Quartics
Let K be a field and f(X) be a separable polynomial in K[X]. The Galois group of f(X) over K permutes the roots of f(X) in a splitting field, and labeling the roots as r1, . . . , rn provides an embedding of the Galois group into Sn. We recall without proof two theorems about this embedding. Theorem 1.1. Let f(X) ∈ K[X] be a separable polynomial of degree n. (a) If f(X) is irreducible in K[X] t...
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We will describe a procedure for figuring out the Galois groups of separable irreducible polynomials in degrees 3 and 4 over fields not of characteristic 2. This does not include explicit formulas for the roots, i.e., we are not going to derive the classical cubic and quartic formulas.
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Collective intelligence, which aggregates the shared information from large crowds, is often negatively impacted by unreliable information sources with the low quality data. This becomes a barrier to the effective use of collective intelligence in a variety of applications. In order to address this issue, we propose a probabilistic model to jointly assess the reliability of sources and find the...
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Treatments of Galois groups of cubic and quartic polynomials usually avoid fields of characteristic 2. Here we will discuss these Galois groups and allow all characteristics. Of course, to have a Galois group of a polynomial we will assume our cubic and quartic polynomials are separable, and to avoid reductions to lower degree polynomials we will assume they are irreducible as well. So our sett...
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Collective human behavior drives a wide range of phenomena in the modern world, from spikes in mobile phone usage1 and online traffic2 to fluctuating demands on transportation3 and emergency response4 infrastructure. However, while the correlated activity of one or two individuals is partially understood5–8, it remains unclear if and how these simple low-order correlations give rise to the comp...
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ژورنال
عنوان ژورنال: Journal of High Energy Physics
سال: 2010
ISSN: 1029-8479
DOI: 10.1007/jhep06(2010)041