  Let A be an m-dimensional vector with positive real entries. Let A_{i,j} be
the vector obtained from A on deleting the entries A_i and A_j. We investigate
some invariant and near invariants related to the solutions E (m-2 dimensional
vectors with entries either +1 or -1) of the linear inequality |A_i-A_j| <
<E,A_{i,J}> < A_i+A_j, where <,> denotes the usual inner product. One of our
methods relates, by the use of Rademacher functions, integrals involving
trigonometric quantities to these quantities.
