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Diophantine Equations and Power Integral Bases [electronic resource] : New Computational Methods /
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.
| Main Authors: | , |
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| Format: | Texto biblioteca |
| Language: | eng |
| Published: |
Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser,
2002
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| Subjects: | Mathematics., Algorithms., Computer science, Mathematics, general., Algorithm Analysis and Problem Complexity., Mathematics of Computing., |
| Online Access: | http://dx.doi.org/10.1007/978-1-4612-0085-7 |
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| Summary: | 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. |
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