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## Section: New Results

### Efficient computation of solution space and conflicts detection for linear systems

Our work on Material Flow Analysis (see e.g. the AF Filières project), involves the analysis of systems of linear inequalities, $l\le Ax\le u$. There are three different but complementary goals for the analysis: (i) given some known variables ${x}_{i}$, efficiently compute the solution space of unknown variables, (ii) if the set of constraints is infeasible, efficiently identify the conflicts, (iii) efficiently classify variables to determine whether they are redundant, just measured, determinable or non-determinable. A baseline implementation for these tasks was available in the team but proved to be too inefficient for larger problem sizes. Through the internship of Alexandre Borthomieu we worked on various improvements, on the algorithmic and implementation side (e.g. choice of programming language), that eventually led to a reduction of execution by three orders of magnitude, compared to the previous implementation.