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Lagrange multiplier To find the extrema of a function f of several variables, subject to the constraint g = 0, one sets ∇f = λ · ∇g. The scalar λ is called a Lagrange multiplier.

Lagrange resolvent Let k be a field of characteristicp containing thenth roots of unity such that p does not divide n. Let k() be an extension field of degree n over k with cyclic Galois group. Let σ be a generator of the Galois group. Let ζ be an nth root of unity. Then the Lagrange resolvent, denoted by (ζ,) is defined by

(ζ,) = 0 + ζ1 + · · · + ζ n−1n−1 wherej = σ j, for each j = 1, 2, . . . , n−1 and n = σn = 0 = .