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Boolean degree of actual point-tensor evaluations

Lax342547.PointQuadratics · concepts/Lax342547/PointQuadratics.lean · lax-342547

proven

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    Natural Language Statement

    Lemma

    The actual base evaluations and pointMoment tensor map have Boolean degree at most two after composition with any linear functional.

    Concept map
    18 concepts; 5 descendants hidden
    100%
    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A
    Evidence

    This concept declares 2 statements. Each proof establishes one of them relative to its assumptions.

    1 base_evaluation_degree proven

    2 point_tensor_evaluation_degree proven

    Lean source view on GitHub

    1import Lax342547.QuadraticDegree
    2import Lax342547.BaseMoments
    3
    4/-!
    5---
    6title: Boolean degree of actual point-tensor evaluations
    7type: lemma
    8---
    9The actual base evaluations and pointMoment tensor map have Boolean degree at most two after composition with any linear functional.
    10-/
    11
    12namespace Lax342547.PointQuadratics
    13
    14open Lax342547.MomentSpace Lax342547.SelectorInterpolation
    15
    16axiom base_evaluation_degree {b : ℕ} (i : Option (Fin b)) :
    17 (fun x : Fin b → Binary => baseEval x i) ∈ selectorSpan b 1
    18
    19axiom point_tensor_evaluation_degree {b : ℕ} {Label Coord : Type} [Fintype Coord]
    20 (p : Label → Coord → Binary) (s : Label)
    21 (φ : Module.Dual Binary (Matrix (Coord × Option (Fin b)) (Coord × Option (Fin b)) Binary)) :
    22 (fun x : Fin b → Binary => φ (pointMoment p s x)) ∈ selectorSpan b 2
    23
    24end Lax342547.PointQuadratics
    25
    Show ProofShow Proof
    Builds on
    Used by
    From Mathlib

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