(参考) https://en.wikipedia.org/wiki/Quintic_function Quintic function (5次方程式) ↓
https://en.wikipedia.org/wiki/Sextic_equation Sextic function (6次方程式) Solvable sextics Some seventh degree equations can be solved by factorizing into radicals, but other septics cannot. Évariste Galois developed techniques for determining whether a given equation could be solved by radicals which gave rise to the field of Galois theory. Some sixth degree equations, such as ax6 + dx3 + g = 0, can be solved by factorizing into radicals, but other sextics cannot. Évariste Galois developed techniques for determining whether a given equation could be solved by radicals which gave rise to the field of Galois theory. It follows from Galois theory that a sextic equation is solvable in terms of radicals if and only if its Galois group is contained either in the group of order 48 which stabilizes a partition of the set of the roots into three subsets of two roots or in the group of order 72 which stabilizes a partition of the set of the roots into two subsets of three roots. There are formulas to test either case, and, if the equation is solvable, compute the roots in term of radicals.[1] References 1. R. Hagedorn, General formulas for solving solvable sextic equations, J. Algebra 233 (2000), 704-757 ↓ つづく
