In algebra, a resolvent cubic is one of several distinct, although related, cubic polynomials defined from a monic polynomial of degree four: P ( x )...

permutation group, in particular: Resolvent quadratic of a cubic equation Resolvent cubic of a quartic equation In logic: Resolvent (logic), the clause produced...

equation. The cubic resolvent of a quartic equation, which is a resolvent for the dihedral group of 8 elements. The Cayley resolvent is a resolvent for the...

finding the roots of the resolvent cubic which is done elsewhere. This resolvent cubic is equivalent to the resolvent cubic given above (equation (1a))...

is one of the roots of a cubic. The solution of the general quartic equation relies on the solution of its resolvent cubic. The eigenvalues of a 3×3...

{\displaystyle S_{4}\to S_{3}} corresponds to the resolvent cubic, in terms of Lagrange resolvents. In the construction of finite rings, eight of the...

corresponding map S4 → S3, corresponds to associating the Lagrange resolvent cubic to a quartic, which allows the quartic polynomial to be solved by radicals...

identifying the three degenerate conics with the three roots of the resolvent cubic. Pappus's hexagon theorem is the special case of Pascal's theorem,...

specific quintic is solvable in radicals can be done by using Cayley's resolvent. This is a univariate polynomial of degree six whose coefficients are...

considered the relation between the roots of a quartic equation and its resolvent cubic. Lagrange's goal (1770, 1771) was to understand why equations of third...

identifying the three degenerate conics with the three roots of the resolvent cubic. For example, given the four points ( ± 1 , ± 1 ) , {\displaystyle...

method, Glasser's method, and the Cockle–Harley method of differential resolvents described below. An alternative form is obtained by setting u = v d 1...

rational coefficients or the polynomial P2 − 1024 z Δ, named Cayley's resolvent, has a rational root in z, where P = z 3 − z 2 ( 20 r + 3 p 2 ) − z (...

method of Lagrange resolvents, which is an early part of Galois theory. This method can be generalized to give the roots of cubic polynomials and quartic...

has the Klein four-group as a normal subgroup. This suggests using a resolvent whose roots may be variously described as a discrete Fourier transform...

Louis Lagrange, in his method of Lagrange resolvents, where he analyzed Cardano's and Ferrari's solution of cubics and quartics by considering them in terms...

series is used in functional analysis. It is closely connected to the resolvent formalism for studying the spectrum of bounded operators and, applied...

Galois theory, this can also be understood in terms of Lagrange resolvents. The resolvent of a quintic is of degree 6—this corresponds to an exotic inclusion...

equations". Made the prescient observation that the roots of the Lagrange resolvent of a polynomial equation are tied to permutations of the roots of the...

Fourier transform or algebraic solutions of algebraic equations (Lagrange resolvent). The n nth roots of unity are the n first powers of ω = e 2 π i n {\displaystyle...

Lagrange, which in the method of Lagrange resolvents used a complex Fourier decomposition to study the solution of a cubic: Lagrange transformed the roots x 1...

вопросах проблемы резольвент" [On certain questions of the problem of resolvents]. Proceedings of Kazan University (in Russian). 114 (2). Kazan University:...