From: wcw@math.psu.edu (William C Waterhouse) Newsgroups: sci.math Subject: Re: solvable quintics ?? Date: 13 Sep 1996 21:33:29 GMT In article gno@selene.rz.uni-duesseldorf.de, rosentha@classic41.rz.uni-duesseldorf.de () writes: > .... by Dummitt ? > Sometime ago i posted a question regarding solvable quintics and was promptly > answered. I received word of an article by "Dummitt" on solvable quintics > en detail in a journal named 'computation and math'. Sadly I was not able to > locate any of the above mentioned data.... Here's the information (taken from mathscinews, the on-line version of Mathematical Reviews): Dummit, D. S. Solving solvable quintics, Mathematics of Computation 57 (1991), 387-401. Corrigenda, Math. Comp. 59 (1992), 309. William C. Waterhouse Penn State ============================================================================== From: Herman Bruyninckx Newsgroups: sci.math.num-analysis Subject: Re: Closed Form Root of Quintic Poly Date: Wed, 4 Nov 1998 08:00:45 +0100 > > Am I wasting time searching for a closed form solution to a degree > > 5 polynomial. I have found refereces for cubic and quartic (if I am > > reading things correctly). > > > > Is there a closed form solution for a quintic polynomial ??? > > Take a look at: @book{King96, author = {King, R. Bruce}, title = {Beyond the quartic equation}, year = {1996}, publisher = {Birkhauser}, address = {Boston, MA}, issn_isbn = {0-8176-3776-1} } @article{KingCanfield91, author = {King, R. Bruce and Canfield, E. Rodney}, title = {An algorithm for calculating the roots of a general quintic equation from its coefficients}, journal = {Journal of Mathematical Physics}, year = {1991}, volume = {32}, pages = {823--825} } @book{Shurman97, author = {Shurman, Jerry M.}, title = {Geometry of the Quintic}, year = {1997}, publisher = {John Wiley \& Sons}, issn_isbn = {0471130176} } @article{Stillwell95, author = {Stillwell, John}, title = {Eisenstein's Footnote}, journal = {The Mathematical Intelligencer}, year = {1995}, volume = {17}, number = {2}, pages = {58--62} } -- Herman.Bruyninckx@mech.kuleuven.ac.be (Ph.D.) Fax: +32-(0)16-32 29 87 Dept. Mechanical Eng., Div. PMA, Katholieke Universiteit Leuven, Belgium ============================================================================== From: Paul Abbott Newsgroups: sci.math.num-analysis Subject: Re: Closed Form Root of Quintic Poly Date: Thu, 05 Nov 1998 11:04:50 +0800 [partial quote of above post deleted -- djr] Also, you might want to take a look at http://www.wolfram.com/posters/quintic/ Not only is the poster very nice there are a good set of references for this problem here. Cheers, Paul ____________________________________________________________________ Paul Abbott Phone: +61-8-9380-2734 Department of Physics Fax: +61-8-9380-1014 The University of Western Australia Nedlands WA 6907 mailto:paul@physics.uwa.edu.au AUSTRALIA http://www.physics.uwa.edu.au/~paul God IS a weakly left-handed dice player ____________________________________________________________________ ============================================================================== From: Robin Chapman Newsgroups: sci.math Subject: Re: Insolubility of quintic without Galois Theory Date: Thu, 26 Nov 1998 08:21:20 GMT In article <73iaqs$t1v$1@nnrp1.dejanews.com>, torquemada@my-dejanews.com wrote: > From the Mathematica web site: > > Finally, Ruffini (1799) and Abel (1826) showed that the solution of > the general quintic cannot be written as > a finite formula involving only the four arithmetic operations and the > extraction of roots. By 1832 Galois > had developed the theory of Galois groups and described exactly when a > polynomial equation is solvable. > > How did Ruffini and Abel show this without Galois theory? Or had they really > discovered the rudiments of Galois theory? According to > http://www-history.mcs.st-and.ac.uk/~history/Mathematicians/Ruffini.html > Ruffini's proof was later called the Wantzel modification of Abel's proof. > Roughly what methods did this use? > In Heinrich D"orrie's 100 Great Problems of Elementary Mathematics (Dover) there's a proof that an irreducible soluble polynomial of odd prime degree p over Q has either 1 real root or p real roots. This proof doesn't use any finite group theory. Perhaps this was the method that Abel & Ruffini used? Robin Chapman + "They did not have proper SCHOOL OF MATHEMATICal Sciences - palms at home in Exeter." University of Exeter, EX4 4QE, UK + rjc@maths.exeter.ac.uk - Peter Carey, http://www.maths.ex.ac.uk/~rjc/rjc.html + Oscar and Lucinda, chapter 20 -----------== Posted via Deja News, The Discussion Network ==---------- http://www.dejanews.com/ Search, Read, Discuss, or Start Your Own