OAI/LinearAlgebra/MatrixMultiplication/AuxiliarySeparation/Arithmetic/RankBound.lean

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The exact-rank exponent bound

Detecting characters exist by Appendix A. The determinant and three-sector polynomial constructions bound the sum of their dot-product exponents by 9/4. Integer rounding then gives the same bound for the exact-rank exponent.

  1. theorem OAI.MatrixMultiplication.AuxiliarySeparation.exactRankExponent_le_nine_quarters line 18

    Source documentation

    The polynomial inequalities bound the actual exact-rank exponent.

    theorem exactRankExponent_le_nine_quarters : exactRankExponent ≤ (9 : ℝ) / 4 := by
    …

    Mentions: OAI.MatrixMultiplication.AuxiliarySeparation.exactRankExponent