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Beyond the Quartic Equation Hardcover – July 30, 1996

ISBN-13: 978-0817637767 ISBN-10: 0817637761 Edition: 1996th

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Editorial Reviews

Review

From the reviews:

"If you want something truly unusual, try [this book] by R. Bruce King, which revives some fascinating, long-lost ideas relating elliptic functions to polynomial equations." --New Scientist

This book presents for the first time a complete algorithm for finding the zeros of any quintic equation based on the ideas of Kiepert. For the sake of completeness, there are chapters on group theory and symmetry, the theory of Galois and elliptic functions. The book ends with considerations on higher degree polynomial equations. --Numerical Algorithms Journal

“The idea of the book at hand is the development of a practicable algorithm to solve quintic equations by means of elliptic and theta functions. … the book can be recommended to anyone interested in the solution of quintic equations.” (Helmut Koch, Zentralblatt MATH, Vol. 1177, 2010)

From the Back Cover

The objective of this book is to present for the first time the complete algorithm for roots of the general quintic equation with enough background information to make the key ideas accessible to non-specialists and even to mathematically oriented readers who are not professional mathematicians. The book includes an initial introductory chapter on group theory and symmetry, Galois theory and Tschirnhausen transformations, and some elementary properties of elliptic function in order to make some of the key ideas more accessible to less sophisticated readers. The book also includes a discussion of the much simpler algorithms for roots of the general quadratic, cubic, and quartic equations before discussing the algorithm for the roots of the general quintic equation. A brief discussion of algorithms for roots of general equations of degrees higher than five is also included.

"If you want something truly unusual, try [this book] by R. Bruce King, which revives some fascinating, long-lost ideas relating elliptic functions to polynomial equations."

--New Scientist

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Product Details

  • Hardcover: 158 pages
  • Publisher: Birkhäuser; 1996 edition (July 30, 1996)
  • Language: English
  • ISBN-10: 0817637761
  • ISBN-13: 978-0817637767
  • Product Dimensions: 6.1 x 0.5 x 9.2 inches
  • Shipping Weight: 15.4 ounces
  • Average Customer Review: 4.5 out of 5 stars  See all reviews (2 customer reviews)
  • Amazon Best Sellers Rank: #3,696,240 in Books (See Top 100 in Books)

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15 of 18 people found the following review helpful By Tom I. on October 11, 1999
Format: Hardcover
King's text is primarily concerned with the theory of finding the roots of a quintic polynomial. He masterfully sets forth a series of transformations based on icosahedral groups, Galois, Tschirnhausen, and other theories. King fails to include a single, practical example, however.
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The problem considered in the book is of great interest and is rarely exposed in modern literature.
The book has pleasing elementary expositions on geometry of groups and galios theory. The description of the use of special functions(theta etc) is good. My only complaint is that I would have liked to see more about equations beyond the quintic. Also it might be fun to see how his code works
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