標題: Titlebook: Diophantine Equations and Power Integral Bases; New Computational Me István Gaál Book 20021st edition Birkh?user Boston 2002 Algebraic Numb [打印本頁] 作者: irritants 時間: 2025-3-21 19:16
書目名稱Diophantine Equations and Power Integral Bases影響因子(影響力)
書目名稱Diophantine Equations and Power Integral Bases影響因子(影響力)學科排名
書目名稱Diophantine Equations and Power Integral Bases網(wǎng)絡(luò)公開度
書目名稱Diophantine Equations and Power Integral Bases網(wǎng)絡(luò)公開度學科排名
書目名稱Diophantine Equations and Power Integral Bases被引頻次
書目名稱Diophantine Equations and Power Integral Bases被引頻次學科排名
書目名稱Diophantine Equations and Power Integral Bases年度引用
書目名稱Diophantine Equations and Power Integral Bases年度引用學科排名
書目名稱Diophantine Equations and Power Integral Bases讀者反饋
書目名稱Diophantine Equations and Power Integral Bases讀者反饋學科排名
作者: 濃縮 時間: 2025-3-21 21:39
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作者: genuine 時間: 2025-3-22 02:41 作者: instill 時間: 2025-3-22 05:17
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作者: Finasteride 時間: 2025-3-22 11:14
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作者: 善于 時間: 2025-3-22 13:02
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作者: 善于 時間: 2025-3-22 17:13 作者: 不易燃 時間: 2025-3-23 00:27
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作者: BRAVE 時間: 2025-3-23 03:33 作者: PACT 時間: 2025-3-23 07:05 作者: largesse 時間: 2025-3-23 12:27
http://image.papertrans.cn/e/image/280541.jpg作者: G-spot 時間: 2025-3-23 15:17
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., Sections 8.3, 10.2, 10.3.1 and 10.3.3.作者: PATHY 時間: 2025-3-23 18:56 作者: 沒花的是打擾 時間: 2025-3-24 00:27 作者: COMMA 時間: 2025-3-24 06:21 作者: 奴才 時間: 2025-3-24 08:53 作者: CUB 時間: 2025-3-24 11:11 作者: Dysarthria 時間: 2025-3-24 17:28
Sextic Fields,An analogue of the general method used for quintic fields, reducing the index form equation directly to unit equations, does not seem to be feasible in sextic fields.作者: surmount 時間: 2025-3-24 22:08
Introduction,s. As we shall see, this algorithmic problem is satisfactorily solved for lower degree number fields (especially for cubic and quartic fields) and there are efficient methods for certain classes of higher degree fields. Our algorithms enable us in many cases to describe all power integral bases also in . of certain number fields.作者: 占卜者 時間: 2025-3-25 02:01
Quartic Fields,ex 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 equations in quartic fields are not much harder to solve than in the cubic case.作者: progestogen 時間: 2025-3-25 07:00
Relative Power Integral Bases,er 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 integral basis over a subfield. Thus, for example the algorithm for relative quartic extensions described in Section 9.3 will be used in octic fields with a quadratic subfield in Section 10.1.作者: 驕傲 時間: 2025-3-25 09:38 作者: GUILE 時間: 2025-3-25 13:47 作者: 亂砍 時間: 2025-3-25 19:12
Book 20021st editionproperties 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.作者: 無能的人 時間: 2025-3-25 21:56
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.978-1-4612-0085-7作者: Infirm 時間: 2025-3-26 04:05
https://doi.org/10.1007/978-1-349-08004-5n Section 7.1. Having read the relatively complicated formulas of this procedure, in Section 7.2 the reader is rewarded with an interesting family of totally real cyclic quintic fields introduced by E.Lehmer.作者: CON 時間: 2025-3-26 05:17
Book 20021st editionng 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 作者: 冥想后 時間: 2025-3-26 10:24
Robert Fisch,Janko Gravner,David Griffeathis chapter we also include an algorithm for solving certain types of norm form equations (Section 3.4), the type of the equation and the ideas for solving it being very close to what we use for the various types of Thue equations.作者: forthy 時間: 2025-3-26 15:15
Auxiliary Equations,is chapter we also include an algorithm for solving certain types of norm form equations (Section 3.4), the type of the equation and the ideas for solving it being very close to what we use for the various types of Thue equations.作者: Inclement 時間: 2025-3-26 16:59
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作者: PALMY 時間: 2025-3-26 21:35 作者: 心胸狹窄 時間: 2025-3-27 05:06
Spatial Linkages of the Chinese Economyex 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 equations in quartic fields are not much harder to solve than in the cubic case.作者: 蹣跚 時間: 2025-3-27 08:09 作者: 貝雷帽 時間: 2025-3-27 13:23
Jin Zhang,Jinkai Li,Xiaotian Wang having subfields. The case of number fields of degree seven seems to be complicated, since these fields can not have subfields. Special number fields of degree seven (e.g., cyclic fields) can be considered by the methods we used so far.作者: flaggy 時間: 2025-3-27 16:45 作者: 折磨 時間: 2025-3-27 21:03 作者: carotenoids 時間: 2025-3-27 22:43
Auxiliary Results, Tools,he reduced bound is usually between 100 and 1000. These reduced bounds are quite modest, however if there are more than 4–5 of them, it is already impossible to test directly all possible exponents with absolute values under the reduced bound. Hence we have to apply certain enumeration methods (Section 2.3) to overcome this difficulty.作者: Gentry 時間: 2025-3-28 04:26 作者: ventilate 時間: 2025-3-28 08:04 作者: 友好 時間: 2025-3-28 11:21
Auxiliary Results, Tools,alled . in two variables of type. + . = 1(cf. equation (2.5)) with given algebraic ., where . are unknown units in a number field. These units are written as a power product of the generators of the unit group and the unknown exponents are to be determined. Baker’s method (Section 2.1) is used to gi作者: anticipate 時間: 2025-3-28 17:41 作者: glomeruli 時間: 2025-3-28 19:13
Index Form Equations in General,rties, 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作者: 積習已深 時間: 2025-3-29 02:40 作者: Patrimony 時間: 2025-3-29 04:45 作者: Estrogen 時間: 2025-3-29 07:58
Relative Power Integral Bases,situation. 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作者: deriver 時間: 2025-3-29 11:43
Some Higher Degree Fields,g; for sextic fields a general algorithm does not seem to be feasible, we developed methods for determining power integral bases only in sextic fields having subfields. The case of number fields of degree seven seems to be complicated, since these fields can not have subfields. Special number fields作者: 造反,叛亂 時間: 2025-3-29 15:57
Tables, algorithms enables us to list the generators of power integral bases for all number fields with small discriminants. We give the data usually in increasing order of discriminants. These data complete other number field data contained in similar tables. Recall, that in the more complicated fields, w作者: Atrium 時間: 2025-3-29 22:03
10樓作者: Terrace 時間: 2025-3-30 03:48
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