Talk:Bring radical

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[edit] Extensions to higher order polynomials

Are there any results for higher polynomials? For example, is it possible to solve a degree 6 polynomial without introducing any further radicals? (This seems plausible, perhaps degree 6 polynomials are either a quintic in disguise, or a cubic of a quadratic) --njh 12:16, 12 July 2006 (UTC)

From what I know, the sextic equation and higher degree polynomial equations cannot be reduced into a single parameter form such as the Bring-Jerrard quintic form, and so their solution is somewhat more complicated. The technique I presented due to M.L. Glasser has been generalized to equations of arbitrarily high degree but using hypergeometric functions of several variables (see here for a German paper). The original quintic solution by Charles Hermite was later generalized to equations of arbitrary degree using Siegel modular forms. --Stormwyrm 03:45, 20 September 2006 (UTC)

[edit] Radicals Disambiguation needed

The link to "radicals" in the third line of this article should be made more specific. Presumably its using one of the four meanings below, but I have no idea which one:

• Radical of an algebraic group, a concept in algebraic group theory
• Radical of an ideal, an important concept in abstract algebra
• Radical of an integer, a concept in number theory
• Radical of a bilinear form, a concept in linear algebra

Could someone who knows fix the link to make it more useful to those who haven't taken math since high school like myself?

Thanks, mennonot 15:44, 8 November 2006 (UTC)