minpoly_natDegree_eq — Mathlib

English

Same as minpoly_natDegree_eq: natDegree(minpoly K a) = ringExpChar K ^ elemExponent K a.

Русский

То же, что и minpoly_natDegree_eq: natDegree(minpoly K a) = ringExpChar K ^ elemExponent K a.

LaTeX

$$natDegree(minpoly K a) = \operatorname{ringExpChar} K^{\operatorname{elemExponent} K a}$$

Lean4

/-- The degree of the minimal polynomial of an element `a ∈ L` equals
`ringExpChar K ^ elemExponent K a`. -/
theorem minpoly_natDegree_eq (a : L) : (minpoly K a).natDegree = ringExpChar K ^ elemExponent K a := by
  rw [minpoly_eq K a, natDegree_sub_C, natDegree_pow, natDegree_X, mul_one]

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