polyCharpoly_natDegree — Mathlib

English

If R is nontrivial, polyCharpoly φ b is nonzero (i.e., it is not the zero polynomial).

Русский

Пусть R ненулевое; polyCharpoly φ b не равен нулю (не тождественно нулевой полином).

LaTeX

$$polyCharpoly_ne_zero$$

Lean4

@[simp]
theorem polyCharpoly_natDegree [Nontrivial R] : (polyCharpoly φ b).natDegree = finrank R M := by
  rw [polyCharpoly, polyCharpolyAux, (charpoly.univ_monic _ _).natDegree_map, charpoly.univ_natDegree,
    finrank_eq_card_chooseBasisIndex]

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