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Bibliographic Details
Main Author:	King, R. Bruce 1938- (Author)
Format:	Book
Language:	English
Published:	Boston [u.a.] Birkhäuser 1996
Subjects:	Equations du cinquième degré Équations du cinquième degré Quintic equations Galois-Theorie Gruppentheorie Algebraische Gleichung Elliptische Funktion Grad 5
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007298340&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Physical Description:	VIII, 149 S. Ill., graph. Darst.
ISBN:	0817637761 3764337761

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Record in the Search Index

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adam_text	Contents Preface vii 1. Introduction 1 2. Group Theory and Symmetry 6 2.1 The Concept of Groups 6 2.2 Symmetry Groups 9 2.3 Regular Polyhedra 13 2.4 Permutation Groups 19 2.5 Polyhedral Polynomials 26 2.6 Transvectants of Polyhedral Polynomials 30 3. The Symmetry of Equations: Galois Theory and Tschirnhausen Transformations 34 3.1 Rings, Fields, and Polynomials 34 3.2 Galois Theory: Solubility of Algebraic Equations by Radicals . 45 3.3 Tschirnhausen Transformations 51 4. Elliptic Functions 56 4.1 Elliptic Functions by the Generalization of Radicals 56 4.2 Elliptic Functions as Doubly Periodic Functions 62 4.3 Theta Functions 72 4.4 Higher Order Theta Functions 79 5. Algebraic Equations Soluble by Radicals 82 5.1 The Quadratic and Cubic Equations 82 5.2 The Quartic Equation 87 5.3 Special Quintic Equations Solvable by Radicals 89 6. The Kiepert Algorithm for Roots of the General Quintic Equation . 95 6.1 Introduction 95 6.2 The Tschirnhausen Transformation of the General Quintic to the Principal Quintic 99 6.3 The Tschirnhausen Transformation of the Principal Quintic to the Brioschi Quintic 103 6.4 Transformation of the Brioschi Quintic to the Jacobi Sextic . 108 6.5 Solution of the Jacobi Sextic with Weierstrass Elliptic Functions 113 6.6 Evaluation of the Weierstrass Elliptic Functions Using Genus 1 Theta Functions 118 6.7 Evaluation of the Periods of the Elliptic Functions Corresponding to the Jacobi Sextic 123 vi Contents 6.8 Undoing the Tschirnhausen Transformations 126 7. The Methods of Hermite and Gordan for Solving the General Quintic Equation 128 7.1 Hermite's Early Work on the Quintic Equation 128 7.2 Gordan's Work on the Quintic Equation 132 8. Beyond the Quintic Equation 139 8.1 The Sextic Equation 139 8.2 The Septic Equation 143 8.3 The General Algebraic Equation of any Degree 147
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spellingShingle	King, R. Bruce 1938- Beyond the quartic equation Equations du cinquième degré ram Équations du cinquième degré Quintic equations Galois-Theorie (DE-588)4155901-0 gnd Gruppentheorie (DE-588)4072157-7 gnd Algebraische Gleichung (DE-588)4001162-8 gnd Elliptische Funktion (DE-588)4134665-8 gnd Grad 5 (DE-588)4366323-0 gnd
subject_GND	(DE-588)4155901-0 (DE-588)4072157-7 (DE-588)4001162-8 (DE-588)4134665-8 (DE-588)4366323-0
title	Beyond the quartic equation
title_auth	Beyond the quartic equation
title_exact_search	Beyond the quartic equation
title_full	Beyond the quartic equation R. Bruce King
title_fullStr	Beyond the quartic equation R. Bruce King
title_full_unstemmed	Beyond the quartic equation R. Bruce King
title_short	Beyond the quartic equation
title_sort	beyond the quartic equation
topic	Equations du cinquième degré ram Équations du cinquième degré Quintic equations Galois-Theorie (DE-588)4155901-0 gnd Gruppentheorie (DE-588)4072157-7 gnd Algebraische Gleichung (DE-588)4001162-8 gnd Elliptische Funktion (DE-588)4134665-8 gnd Grad 5 (DE-588)4366323-0 gnd
topic_facet	Equations du cinquième degré Équations du cinquième degré Quintic equations Galois-Theorie Gruppentheorie Algebraische Gleichung Elliptische Funktion Grad 5
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007298340&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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Call Number:	0102 MAT 145f 2001 A 20638 Floor plan
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