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Symmetric VNP

Lax461425.SymmetricVNPCharacterisation · concepts/Lax461425/SymmetricVNPCharacterisation.lean · lax-461425

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    Natural Language Statement

    Theorem

    Over a field of characteristic zero, symmetric VNP consists precisely of the families of matrix-invariant polynomials.

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    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A
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    1import Lax461425.BooleanSumSymmetry
    2import Lax461425.SymmetricFormulaWitness
    3
    4/-!
    5---
    6title: Symmetric VNP
    7type: theorem
    8---
    9Over a field of characteristic zero, symmetric VNP consists precisely of the families
    10of matrix-invariant polynomials.
    11-/
    12
    13namespace Lax461425.SymmetricVNPCharacterisation
    14
    15open SymmetricFamilies SymmetricClasses SymmetricVNP
    16
    17/-- Symmetric VNP consists precisely of all matrix-invariant polynomial families. -/
    18axiom all_matrix_symmetric_iff {K : Type*} [Field K] [CharZero K] (f : MatrixFamily K) :
    19 InSymVNP f ↔ ∀ n, MatrixInvariant (f n)
    20
    21end Lax461425.SymmetricVNPCharacterisation
    22
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