Wang, Lianxiang Simultaneous diophantine approximation. (English) Zbl 0746.11028 Sci. China, Ser. A 34, No. 10, 1153-1161 (1991). From the author’s summary: “Several existence and effective results for theorems of Dirichlet and Minkowski on simultaneous Diophantine approximation in the homogeneous case (including \(p\)-adic and \(p\)-adic- real mixed cases) are given. ”The paper includes a theorem on a polynomial time algorithm to find integer solutions of such diophantine inequalities based on the \(LLL\)- basis reduction algorithm together with an application of the algorithm in a concrete case. Reviewer: R.Wallisser (Freiburg i.Br.) MSC: 11J13 Simultaneous homogeneous approximation, linear forms 11Y16 Number-theoretic algorithms; complexity 11J61 Approximation in non-Archimedean valuations 11J25 Diophantine inequalities Keywords:diophantine approximation; Dirichlet theorem; basis reduction algorithm; Minkowski linear form theorem Citations:Zbl 0687.10026 PDFBibTeX XMLCite \textit{L. Wang}, Sci. China, Ser. A 34, No. 10, 1153--1161 (1991; Zbl 0746.11028)