OAI/NumberTheory/Ostmann/Construction/ExpandedHistoryFormula.lean

GitHub source file

8 declarations, 0 contain sorry, 0 declared as axioms

History formulas on the original independent prime variables

Internal pivot addresses are initialized to one. Substitution removes them from the polynomial variable type before the prime-divisibility estimate.

  1. def OAI.Ostmann.HistoryFormula.originalPrimes line 17
  2. theorem OAI.Ostmann.HistoryFormula.originalPrimes_value line 21
  3. theorem OAI.Ostmann.HistoryFormula.originalPrimes_cost line 31
  4. theorem OAI.Ostmann.HistoryFormula.originalPrimes_frequencies line 42
  5. theorem OAI.Ostmann.HistoryFormula.originalPrimes_denominator line 51
  6. theorem OAI.Ostmann.HistoryFormula.originalPrimes_inputs line 57
  7. theorem OAI.Ostmann.HistoryFormula.originalPrimes_integer_value line 67

    Source documentation

    The actual reconstructed integer and its collapsed polynomial have exactly the same numerator, up to their common small-frequency denominator.

    theorem originalPrimes_integer_value {V : Type*} {n : ℕ}
    (F : HistoryFormula (ExpandedScheduledVariable V n)) (x : V → ℤ) (y : ℤ)
    (hy : F.value (fun i => (expandedPrimeValues n x i : ℚ)) = y) :
    MvPolynomial.eval₂Hom (RingHom.id ℤ) x F.originalPrimes.cleared.numerator =
      F.cleared.denominator * y := by
…

    Mentions: OAI.Ostmann.HistoryFormula, OAI.Ostmann.ExpandedScheduledVariable, OAI.Ostmann.expandedPrimeValues

  8. theorem OAI.Ostmann.HistoryFormula.originalPrimes_coprime line 76