Beyond the quartic equation:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser
1996
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 149 S. Ill., graph. Darst. |
| ISBN: | 0817637761 3764337761 |
Staff View
MARC
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| 245 | 1 | 0 | |a Beyond the quartic equation |c R. Bruce King |
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 1996 | |
| 300 | |a VIII, 149 S. |b Ill., graph. Darst. | ||
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| 650 | 4 | |a Quintic equations | |
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Record in the Search Index
| _version_ | 1828141280927940608 |
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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 |
| any_adam_object | 1 |
| author | King, R. Bruce 1938- |
| author_GND | (DE-588)114678839 |
| author_facet | King, R. Bruce 1938- |
| author_role | aut |
| author_sort | King, R. Bruce 1938- |
| author_variant | r b k rb rbk |
| building | Verbundindex |
| bvnumber | BV010910371 |
| callnumber-first | Q - Science |
| callnumber-label | QA215 |
| callnumber-raw | QA215 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 180 |
| classification_tum | MAT 145f MAT 146f |
| ctrlnum | (OCoLC)845182064 (DE-599)BVBBV010910371 |
| dewey-full | 512.9/42 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.9/42 |
| dewey-search | 512.9/42 |
| dewey-sort | 3512.9 242 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV010910371 |
| illustrated | Illustrated |
| indexdate | 2025-03-31T20:03:06Z |
| institution | BVB |
| isbn | 0817637761 3764337761 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007298340 |
| oclc_num | 845182064 |
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| physical | VIII, 149 S. Ill., graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Birkhäuser |
| record_format | marc |
| spelling | King, R. Bruce 1938- Verfasser (DE-588)114678839 aut Beyond the quartic equation R. Bruce King Boston [u.a.] Birkhäuser 1996 VIII, 149 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Equations du cinquième degré ram Équations du cinquième degré Quintic equations Galois-Theorie (DE-588)4155901-0 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Algebraische Gleichung (DE-588)4001162-8 gnd rswk-swf Elliptische Funktion (DE-588)4134665-8 gnd rswk-swf Grad 5 (DE-588)4366323-0 gnd rswk-swf Algebraische Gleichung (DE-588)4001162-8 s Grad 5 (DE-588)4366323-0 s Galois-Theorie (DE-588)4155901-0 s Gruppentheorie (DE-588)4072157-7 s Elliptische Funktion (DE-588)4134665-8 s DE-604 HBZ Datenaustausch application/pdf 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 Inhaltsverzeichnis |
| 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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