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Mathlib.Tactic.Linarith.Oracle.SimplexAlgorithm

The oracle based on Simplex Algorithm #

This file contains hooks to enable the use of the Simplex Algorithm in linarith. The algorithm's entry point is the function Linarith.SimplexAlgorithm.findPositiveVector. See the file PositiveVector.lean for details of how the procedure works.

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def Linarith.SimplexAlgorithm.preprocess (matType : ℕ → ℕ → Type) [Linarith.SimplexAlgorithm.UsableInSimplexAlgorithm matType] (hyps : List Linarith.Comp) (maxVar : ℕ) :
matType (maxVar + 1) hyps.length × List ℕ

Preprocess the goal to pass it to Linarith.SimplexAlgorithm.findPositiveVector.

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    def Linarith.SimplexAlgorithm.postprocess (vec : Array ℚ) :
    Std.HashMap ℕ ℕ

    Extract the certificate from the vec found by Linarith.SimplexAlgorithm.findPositiveVector.

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      def Linarith.CertificateOracle.simplexAlgorithmSparse :
      Linarith.CertificateOracle

      An oracle that uses the Simplex Algorithm.

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        def Linarith.CertificateOracle.simplexAlgorithmDense :
        Linarith.CertificateOracle

        The same oracle as CertificateOracle.simplexAlgorithmSparse, but uses dense matrices. Works faster on dense states.

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