I am not sure if this question has been already done but I could not find it. Given a[1], a[2], ..., a[n] real, non-rational algebraic values, and R > 0 a (small) real value, is there an efficient algorithm to find all sets of integer values i[1], i[2], ..., i[n] such that | i[1]a[1] + i[2]a[2] + ... + i[n]a[n] | < R ? I have done it by brute force but I cannot go beyond n > 6. Any comments on this subject is appreciated. Continue reading...
