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Mathlib.Tactic.Linarith.Oracle.SimplexAlgorithm.Gauss

Gaussian Elimination algorithm #

The first step of Linarith.SimplexAlgorithm.findPositiveVector is finding initial feasible solution which is done by standard Gaussian Elimination algorithm implemented in this file.

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@[reducible, inline]
abbrev Linarith.SimplexAlgorithm.Gauss.GaussM (n m : Nat) (matType : Nat → Nat → Type) (α : Type) :
Type

The monad for the Gaussian Elimination algorithm.

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    def Linarith.SimplexAlgorithm.Gauss.findNonzeroRow {n m : Nat} {matType : Nat → Nat → Type} [Linarith.SimplexAlgorithm.UsableInSimplexAlgorithm matType] (rowStart col : Nat) :
    Linarith.SimplexAlgorithm.Gauss.GaussM n m matType (Option Nat)

    Finds the first row starting from the rowStart with nonzero element in the column col.

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      def Linarith.SimplexAlgorithm.Gauss.getTableauImp {n m : Nat} {matType : Nat → Nat → Type} [Linarith.SimplexAlgorithm.UsableInSimplexAlgorithm matType] :
      Linarith.SimplexAlgorithm.Gauss.GaussM n m matType (Linarith.SimplexAlgorithm.Tableau matType)

      Implementation of getTableau in GaussM monad.

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        def Linarith.SimplexAlgorithm.Gauss.getTableau {n m : Nat} {matType : Nat → Nat → Type} [Linarith.SimplexAlgorithm.UsableInSimplexAlgorithm matType] (A : matType n m) :
        Lean.CoreM (Linarith.SimplexAlgorithm.Tableau matType)

        Given matrix A, solves the linear equation A x = 0 and returns the solution as a tableau where some variables are free and others (basic) variable are expressed as linear combinations of the free ones.

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