OAI/Analysis/MutuallyUnbiased/Cubic/CubicMultiplicityCore.lean

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4 declarations, 0 contain sorry, 0 declared as axioms

Multiplicity counting once the two possible cubed values are known.

  1. theorem OAI.MUB6.unit_cube_mul_conj_square line 12
  2. def OAI.MUB6.cubeClass line 18
  3. theorem OAI.MUB6.same_cube_zero_sum_card_ge_three line 25

    Source documentation

    A nonempty zero-sum collection of nonzero numbers with the same cube has at least three members: one term cannot vanish, and two opposite terms have opposite cubes.

    theorem same_cube_zero_sum_card_ge_three (v : (Fin 6) → ℂ) (s : Finset (Fin 6))
        (a : ℂ) (ha : a ≠ 0) (hne : s.Nonempty)
        (hcube : ∀ i ∈ s, v i ^ 3 = a) (hsum : ∑ i ∈ s, v i = 0) :
        3 ≤ s.card := by
    …
  4. theorem OAI.MUB6.two_cube_classes_card_three line 50