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Solving the Quintic with Mathematica, A Poster

  • To: mathgroup at
  • 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

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

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 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 or by World Wide Web at

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