  We present a polynomial-time algorithm that obtains a set of Asymptotic
Linear Programs (ALPs) from a given linear system S, such that one of these
ALPs admits a feasible solution if and only if S admits a feasible solution. We
also show how to use the same algorithm to determine whether or not S admits a
non-trivial solution for any desired subset of its variables. S is allowed to
consist of linear constraints over real variables with integer coefficients,
where each constraint has either a lesser-than-or-equal-to, or a lesser-than,
or a not-equal-to relational operator. Each constraint of the obtained ALPs has
a lesser-than-or-equal-to relational operator, and the coefficients of its
variables vary linearly with respect to the time parameter that tends to
positive infinity.

Computational Complexity;Discrete Mathematics;Algebraic Geometry