Solving the Quintic with Mathematica, A Poster
- To: mathgroup at christensen.cybernetics.net
- Subject: [mg265] Solving the Quintic with Mathematica, A Poster
- From: orders (Wolfram Research)
- Date: Thu, 01 Dec 1994 16:07:42 -0600
Solving the Quintic with Mathematica, A Poster All mathematicians know that there is no formula for the solution of the general quintic, a x^5 + b x^4 + c x^3 + d x^2 + e x + f == 0. Or do they? The story of the solution of the quintic didn't end when Ruffini, Abel, and Galois showed that there is no algebraic solution to the quintic at the beginning of the 19th century. That's because in 1858, Hermite, Kronecker, and Brioschi independently discovered solutions in terms of elliptic modular functions, and Klein discovered a solution in terms of hypergeometric functions. The hypergeometric functions are built into Mathematica and the elliptic modular functions are easy to define. It seemed only natural for Wolfram Research's research and development team to program the methods of these mathematicians as an acid test of new technology in Mathematica. Little did they know how difficult this would be! They were very fortunate to have the extensive library resources of the University of Illinois. The result appears in the poster, "Solving the Quintic with Mathematica," which features the history behind several solutions to the quintic. Included is a description of how formulas for the quintic were derived and their implementation in Mathematica. Pictures of Riemann surfaces are among the several different kinds of graphics illustrating the mathematics. The poster also includes a detailed historical time line of the solution of polynomial equations in one variable with more than one hundred entries. It shows portraits of many of the world's most famous mathematicians and describes their contributions to our understanding of this important subject. The poster was created for the International Congress of Mathematicians held this summer in Zurich, Switzerland. It was distributed to over 3,000 attending mathematicians at the conference computer lab (sponsored by Wolfram Research). This large, well-made poster is colorful, fascinating, and informative. For information on how to order the poster for a nominal price, telephone customer service at (+)1-217-398-5151 or email orders at wri.com. You can find the complete text for the poster, as well as an extensive bibliography and the source code for the pictures on MathSource; there is no cost for this. For information about how to get the text, send the email message "Help Intro" to mathsource at wri.com. The MathSource item numbers are 0207-199 for the NeXT and Macintosh and 0207-122 for other systems. They are located in the /pub/WhatsNew directory. You can also access the quintic documents by anonymous ftp or Gopher at mathsource.wri.com or by World Wide Web at http://www.wri.com/MathSource.html.