Fast computation of class fields given their norm group.

Let K be a number field containing, for some prime ℓ, the ℓ-th roots of unity. Let L be a Kummer extension of degree ℓ of K characterized by its modulus m and its norm group. Let Kmbe the compositum of degree ℓ extensions of K of conductor dividing m. Using the vector-space structure of Gal(Km/K), we suggest a modification of the rnfkummer function of PARI/GP which brings the complexity of the computation of an equation of L over K from exponential to linear.