New Korkin-Zoloratev inequalities : implementation and numerical data

This technical report discusses the mathematical details and the implementation of the methods discussed in the accompanying paper [PZ06]. In particular a method to find a finite list of inequalities that certify Korkin–Zolotarev reducedness of a quadratic form is presented. Moreover a semidefinite programming relaxation of the space of KZ-reduced quadratic forms is described in detail, together with a branching strategy to optimize over this space. Finally the implementation of these methods is discussed, together with some hints on how to compile and use the programs. The two digital appendices, which can be obtained from the SPOR reports website†, contain an implementation of the methods discussed and numerical data that prove the theorems in [PZ06].