I know how to solve a set of linear equalities with Gauss-Jordan elimination, but this gives me all real solutions. Is there a way to constrain all variables to the non-negative integers, i.e., $x \in \mathbb N$?
2026-03-28 20:13:38.1774728818
Use Gauss-Jordan elimination to solve a linear system for non-negative integer solutions?
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This is called integer programming. This is a huge complex field, with some of the common approaches being branch and bound and cutting plane methods. See the wiki links for more information.