All mathematicians know that there is no formula for the solution of the general quintic equation:
5 4 3 2 a x + b x + c x + d x + e x + f = 0Or 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. That's because later in the 19th century, 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 being implemented for the forthcoming release. It seemed only natural for Wolfram Research's Research and Development group to program the methods of these mathematicians as an acid test of the new technology. 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. The poster also includes a detailed historical time line of the solution of polynomial equations in one variable. It shows portraits of many of the world's most famous mathematicians and describes their contributions to our understanding of this important subject.
Created for the International Congress of Mathematicians held this summer in Zurich, Switzerland, the poster was distributed to over 3,000 attending mathematicians at the conference computer lab, which was sponsored by Wolfram Research. A limited supply of these posters is now available.
View a clickable image map of the Solving the Quintic with Mathematica poster.
27 inch X 38 inch poster.
Price: $10.
To order this item, see the order form.
