OAI/NumberTheory/DukePrimeDegree/Geometry/QuotientLogDistance.lean

GitHub source file

12 declarations, 0 contain sorry, 0 declared as axioms

Logarithmic displacement distance on the lattice quotient

Taking the infimum over actual right translations gives a distance independent of a representative. Its triangle inequality and translation bound provide uniformly controlled real observables on the quotient.

  1. lemma OAI.DukePrimeDegree.exists_rightAction_eq line 19
  2. def OAI.DukePrimeDegree.rightDisplacementLengths line 28
  3. lemma OAI.DukePrimeDegree.rightDisplacementLengths_nonempty line 31
  4. lemma OAI.DukePrimeDegree.rightDisplacementLengths_bddBelow line 36
  5. def OAI.DukePrimeDegree.quotientLogDistance line 42
  6. lemma OAI.DukePrimeDegree.quotientLogDistance_nonneg line 44
  7. lemma OAI.DukePrimeDegree.quotientLogDistance_le_length line 49
  8. lemma OAI.DukePrimeDegree.quotientLogDistance_self line 53
  9. lemma OAI.DukePrimeDegree.quotientLogDistance_triangle line 57
  10. lemma OAI.DukePrimeDegree.quotientLogDistance_symm line 75
  11. theorem OAI.DukePrimeDegree.quotientLogDistance_right_bound line 86

    Source documentation

    The distance from a fixed point changes by at most the length of a right translation, uniformly in the point being translated.

    theorem quotientLogDistance_right_bound {n : ℕ} (x y : X n) (g : G n) :
    |quotientLogDistance x (rightAction y g)-quotientLogDistance x y| ≤ matrixLogLength g := by
…

    Mentions: OAI.DukePrimeDegree.quotientLogDistance, OAI.DukePrimeDegree.matrixLogLength

  12. lemma OAI.DukePrimeDegree.exists_rightAction_length_lt line 94