Please use this identifier to cite or link to this item: http://scholarbank.nus.edu.sg/handle/10635/14460
Title: On solvable septics
Authors: LAU JING FENG
Keywords: septics, quintics, radicals
Issue Date: 7-Jan-2005
Source: LAU JING FENG (2005-01-07). On solvable septics. ScholarBank@NUS Repository.
Abstract: The problem of solving the general irreducible polynomial in one variable and expressing its roots in radicals has been proposed ages ago. Since then the case of solving general quadratics, cubics and quartics has been solved and it took a few centuries before Abel and Galois demonstrated the impossibility to solve general equations of degree higher than 4. In two recent papers [D] and [H], Dummit and respectively Hagedorn provide methodologies to solve the general solvable quintic and sextic. In this thesis, we shall adopt the techniques in [D] to give a qualitative description of solving solvable irreducible polynomials of arbitrary prime degree and apply these results to solve for two of the roots of x^7+x^6-12x^5-7x^4+28x^3+14x^2-9x+1=0 which can be used to express cos 2 pi/29 in radicals.References[D] D. S. Dummit, Solving Solvable Quintics, Mathematics of Computation, Volume 57, Issue 195, 387-401, 1991.[H] T. R. Hagedorn, General Formulas for Solving Solvable Sextic Equations, Journal of Algebra, Volume 233, Issue 2, 704-757, 2000.
URI: http://scholarbank.nus.edu.sg/handle/10635/14460
Appears in Collections:Master's Theses (Open)

Show full item record
Files in This Item:
File Description SizeFormatAccess SettingsVersion 
LauJF.pdf319.92 kBAdobe PDF

OPEN

NoneView/Download

Page view(s)

487
checked on Dec 11, 2017

Download(s)

595
checked on Dec 11, 2017

Google ScholarTM

Check


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.