Simplex-Module Algorithm for Expansion of Algebraic Numbers in Multidimensional Continued Fractions

详细

The simplex-module algorithm for expansion of algebraic numbers α = (α₁, . . . , α_d) in multidimensional continued fractions is suggested. The method is based on minimal rational simplices s, where α ∈ s, and Pisot matrices P_α, for which \( \widehat{\alpha} \) = (α₁, . . . , α_d, 1) is an eigenvector. A multidimensional generalization of the Lagrange theorem is proved.