OAI/NumberTheory/Ostmann/Construction/HistoryPolynomialSpecialization.lean

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6 declarations, 0 contain sorry, 0 declared as axioms

Actual cleared history polynomials with one prime left variable

  1. def OAI.Ostmann.specializeHistoryVariable line 13
  2. theorem OAI.Ostmann.specializeHistoryVariable_eval line 18
  3. theorem OAI.Ostmann.specializeHistoryVariable_natDegree line 33

    Source documentation

    Fixing all the other prime variables cannot increase the degree. The bound comes from the original monomial support, so cancellation is harmless.

    theorem specializeHistoryVariable_natDegree {σ : Type*}
    (P : MvPolynomial σ ℤ) (a : σ → ℝ) (i : σ) :
    (specializeHistoryVariable a i P).natDegree ≤ P.totalDegree := by
…

    Mentions: OAI.Ostmann.specializeHistoryVariable

  4. def OAI.Ostmann.normalizedHistoryPolynomial line 62
  5. theorem OAI.Ostmann.normalizedHistoryPolynomial_eval line 66
  6. theorem OAI.Ostmann.normalizedHistoryPolynomial_natDegree line 74