OAI/NumberTheory/Ostmann/Arithmetic/ClearedPolynomialRanges.lean

GitHub source file

6 declarations, 0 contain sorry, 0 declared as axioms

1. def OAI.Ostmann.clearedIntervalPolynomials line 12
2. def OAI.Ostmann.clearedIntervalKeep line 17
3. theorem OAI.Ostmann.cleared_interval_test line 19
4. theorem OAI.Ostmann.clearedIntervalKeep_iff line 28
5. theorem OAI.Ostmann.clearedIntervalPolynomials_degree line 36
6. theorem OAI.Ostmann.specialized_cleared_interval_test line 51

   Source documentation

   Fixing the other primes gives the literal range test on the cleared history numerator. Denominator signs require no separate cases.

   theorem specialized_cleared_interval_test {σ : Type*} (P : MvPolynomial σ ℤ)
       (a : σ → ℝ) (i : σ) (d lo hi x : ℝ) (hd : d ≠ 0) :
       clearedIntervalKeep (polynomialSupportCode
         (clearedIntervalPolynomials (specializeHistoryVariable a i P) d lo hi) x) = true ↔
       MvPolynomial.eval₂ (Int.castRingHom ℝ) (Function.update a i x) P / d ∈ Set.Icc lo hi := by
   …

   Mentions: OAI.Ostmann.clearedIntervalKeep, OAI.Ostmann.polynomialSupportCode, OAI.Ostmann.clearedIntervalPolynomials, OAI.Ostmann.specializeHistoryVariable