OAI/Analysis/MutuallyUnbiased/Cubic/CubicMultiplicityCore.lean
4 declarations, 0 contain sorry, 0 declared as axioms
Multiplicity counting once the two possible cubed values are known.
- theorem
OAI.MUB6.unit_cube_mul_conj_squareline 12 - def
OAI.MUB6.cubeClassline 18 - theorem
OAI.MUB6.same_cube_zero_sum_card_ge_threeline 25Source 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 … - theorem
OAI.MUB6.two_cube_classes_card_threeline 50