From: mckay@cs.concordia.ca (MCKAY john)
Subject: Re: How to do a TSCHIRNHAUSEN transformation?
Date: 16 Apr 2000 12:44:36 GMT
Newsgroups: sci.math
Summary: [missing]

In article <vi1pwluvecu2@forum.mathforum.com>,
Tito Piezas III <abelard_x@hotmail.com> wrote:
>April 16, 2000
>
>I need help with an algebraic problem.  How do you a Tschirnhausen
>transformation? Does it involve radicals?
>
>I know that it can eliminate as many as 3 terms in a polynomial and
>that it is supposed to be a generalization of a Viete transform (which
>can eliminate the x^n-1 term). That i can easily do but it's hard to
>find how to do the Tshirnhausen.
>
>Can you use the Tschirnhausen to solve the cubic casus irreducibilis
>in radicals?
>
>Sincerely,
>
>Tito Piezas III

Try a resultant     resultant( f(x), y-t(x),x) where f(x) is your polynomial
and =t(x) is your Tschirnhaus transformation.

There are few definitions of Tchirnhaus transformations in the literature.

The idea is that the splitting field of a polynomials is unchanged if we
replace its variable by an invertible rational expression. This can be
expressed as a polynomial, y = t(x).

JM

-- 
But leave the wise to wrangle, and with me
the quarrel of the universe let be;
and, in some corner of the hubbub couched,
make game of that which makes as much of thee.