OAI/LinearAlgebra/CirculantHadamard/CyclicEvaluationProjection.lean

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Evaluation at a root of smaller order factors through the cyclic quotient.

  1. theorem OAI.CirculantHadamard.evaluateAt_cyclicProjection line 21

    Source documentation

    The actual root evaluation is unchanged after reducing the cyclic index. Both root equations are stated explicitly to match the two evaluation maps.

    theorem evaluateAt_cyclicProjection (h : m ∣ n)
        (x : S) (hm : x ^ m = 1) (hn : x ^ n = 1) (F : Elem R n) :
        evaluateAt m x hm (cyclicProjection R h F) = evaluateAt n x hn F := by
    …

    Mentions: OAI.CirculantHadamard.cyclicProjection