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Field name	Details
Dewey Class	512.7
Title	Diophantine Equations and Power Integral Bases ([EBook]) : New Computational Methods / by István Gaál.
Author	Gaál, István
Other name(s)	SpringerLink (Online service)
Publication	Boston, MA : Birkhäuser , 2002.
Physical Details	208 pages : online resource.
ISBN	9781461200857
Contents note	1 Introduction -- 1.1 Basic concepts -- 1.2 Related results -- 2 Auxiliary Results, Tools -- 2.1 Baker’s method, effective finiteness theorems -- 2.2 Reduction -- 2.3 Enumeration methods -- 2.4 Software, hardware -- 3 Auxiliary Equations -- 3.1 Thue equations -- 3.2 Inhomogeneous Thue equations -- 3.3 Relative Thue equations -- 3.4 The resolution of norm form equations -- 4 Index Form Equations in General -- 4.1 The structure of the index form -- 4.2 Using resolvents -- 4.3 Factorizing the index form when proper subfields exist -- 4.4 Composite fields -- 5 Cubic Fields -- 5.1 Arbitrary cubic fields -- 5.2 Simplest cubic fields -- 6 Quartic Fields -- 6.1 Algorithm for arbitrary quartic fields -- 6.2 Simplest quartic fields -- 6.3 An interesting application to mixed dihedral quartic fields -- 6.4 Totally complex quartic fields -- 6.5 Bicyclic biquadratic number fields -- 7 Quintic Fields -- 7.1 Algorithm for arbitrary quintic fields -- 7.2 Lehmer’s quintics -- 8 Sextic Fields -- 8.1 Sextic fields with a quadratic subfield -- 8.2 Sextic fields with a cubic subfield -- 8.3 Sextic fields as composite fields -- 9 Relative Power Integral Bases -- 9.1 Basic concepts -- 9.2 Relative cubic extensions -- 9.3 Relative quartic extensions -- 10 Some Higher Degree Fields -- 10.1 Octic fields with a quadratic subfield -- 10.2 Nonic fields with cubic subfields -- 10.3 Some more fields of higher degree -- 11 Tables -- 11.1 Cubic fields -- 11.2 Quartic fields -- 11.3 Sextic fields -- References -- Author Index.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-1-4612-0085-7
Links to Related Works	Subject References: Algorithm Analysis and Problem Complexity . Algorithms . Mathematics . Mathematics, general . Mathematics of Computing . Number Theory . Authors: Gaál, István . Corporate Authors: SpringerLink (Online service) . Classification: 512.7 . 512.7 (DDC 22) .

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Diophantine Equations and Power Integral Bases: New Computational Methods

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