Tschirnhausen Transformation

A transformation of a polynomial equation  which is of the form  where  and  are polynomials and  does not vanish at a root of . The cubic equation is a special case of such a transformation. Tschirnhaus (1683) showed that a polynomial of degree  can be reduced to a form in which the  and  terms have 0 coefficients. In 1786, E. S. Bring showed that a general quintic equation can be reduced to the form

In 1834, G. B. Jerrard showed that a Tschirnhaus transformation can be used to eliminate the , , and terms for a general polynomial equation of degree .

REFERENCES:

Boyer, C. B. A History of Mathematics. New York: Wiley, pp. 472-473, 1968.

Tschirnhaus. Acta Eruditorum. 1683.