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On Fourier's algorithm for linear arithmetic constraints

Abstract

In the 1820s Fourier provided the first algorithm for solving linear arithmetic constraints. In other words, this algorithm determines whether or not the polyhedral set associated with the constraints is empty. We show here that Fourier's algorithm has an important hidden property: in effect it also computes the affine hull of the polyhedral set. This result is established by making use of a recent theorem on the independence of negative constraints.

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Lassez, J., Maher, M.J. On Fourier's algorithm for linear arithmetic constraints. Journal of Automated Reasoning 9, 373–379 (1992). https://doi.org/10.1007/BF00245296

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Key words

  • Linear arithmetic
  • Fourier's algorithm
  • implicit equality
  • affine hull