I'm working on rational number field $\mathbb{Q}$.
Is there an efficient algorithm finding a solution of system of linear inequalities?
In many computer algebra systems like Sage or Maple,
there are functions finding the whole solution set, but in my problem (approximately 40 dimensional vector space with 600 inequalities) it seems that the computation is too heavy. Also, in my situation I don't need the whole set – just a single solution is sufficient.
What is a good method to find a solution?
Best Answer
You can do linear programming (for example, by giving it a random objective function); this will return a feasible solution - in fact, a vertex of the solution set. You can run such a linear program in maple (and possibly in sage). For something faster see the exact rational LP solver at http://www2.isye.gatech.edu/~wcook/qsopt/ex/index.html