# Efficient algorithm finding 'a' solution of system of linear inequalities

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?

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Mathematica has a function called FindInstance that looks for a single solution satisfying a set of specified criteria. –  Yoav Kallus Feb 12 at 0:14