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Titlebook: Diophantine Equations and Power Integral Bases; New Computational Me István Gaál Book 20021st edition Birkh?user Boston 2002 Algebraic Numb

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樓主
發(fā)表于 2025-3-21 19:16:26 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書目名稱Diophantine Equations and Power Integral Bases
副標(biāo)題New Computational Me
編輯István Gaál
視頻videohttp://file.papertrans.cn/281/280541/280541.mp4
圖書封面Titlebook: Diophantine Equations and Power Integral Bases; New Computational Me István Gaál Book 20021st edition Birkh?user Boston 2002 Algebraic Numb
描述This monograph investigates algorithms for determining power integral bases in algebraic number fields. It introduces the best-known methods for solving several types of diophantine equations using Baker-type estimates, reduction methods, and enumeration algorithms. Particular emphasis is placed on properties of number fields and new applications. The text is illustrated with several tables of various number fields, including their data on power integral bases. Good resource for solving classical types of diophantine equations. Aimed at advanced undergraduate/graduate students and researchers.
出版日期Book 20021st edition
關(guān)鍵詞Algebraic Number Theory; Algorithmic Analysis; Finite; Mathematics of Computing; algebra; algorithms; calc
版次1
doihttps://doi.org/10.1007/978-1-4612-0085-7
isbn_ebook978-1-4612-0085-7
copyrightBirkh?user Boston 2002
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發(fā)表于 2025-3-21 21:39:06 | 只看該作者
Robert Fisch,Janko Gravner,David Griffeathcase 1, α,...,α. is an integral basis of ., called a .. Our main task is to develop algorithms for determining all generators α of power integral bases. As we shall see, this algorithmic problem is satisfactorily solved for lower degree number fields (especially for cubic and quartic fields) and the
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地板
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Robert Fisch,Janko Gravner,David Griffeathl see in the following chapters, various types of Thue equations play an essential role in the resolution of index form equations [Ga96b]. We summarize the methods for the resolution of these equations in this chapter. We shall consider Thue equations (Section 3.1), inhomogeneous Thue equations (Sec
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發(fā)表于 2025-3-22 11:14:23 | 只看該作者
Kenneth S. Alexander,Joseph C. Watkinsrties, makes the resolution of index form equations much easier. A special situation (which otherwise is frequent in numerical examples) is considered in Section 4.4, when the field . is the composite of its subfields. The general results on composite fields have several applications, see e.g., Sect
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發(fā)表于 2025-3-22 13:02:52 | 只看該作者
Spatial Linkages of the Chinese Economybles. The resolution of such an equation can yield a difficult problem. The main goal of this Chapter is to point out that in the quartic case the index form equation can be reduced to a cubic and some corresponding quartic Thue equations (see Section 6.1). This means that in fact the index form equ
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發(fā)表于 2025-3-23 00:27:37 | 只看該作者
Visualizing Classic Chinese Literaturesituation. The algorithms for determining generators of relative power integral bases will be applied for finding generators of integral bases in higher degree fields having subfields. It is easy to see that if an element generates a power integral basis, then it also generates a relative power inte
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