English
Compatibility of polyCharpolyAux under the map to the matrix charpoly holds in multiple configurations.
Русский
Согласованность polyCharpolyAux при отображении в матричный характеристический полином сохраняется во множестве конфигураций.
LaTeX
$$Same as polyCharpolyAux_map_eq_charpoly for variant x.$$
Lean4
/-- Let `L` and `M` be finite free modules over `R`,
and let `φ : L →ₗ[R] Module.End R M` be a linear family of endomorphisms.
Let `b` be a basis of `L` and `bₘ` a basis of `M`.
Then `LinearMap.polyCharpoly φ b` is the polynomial that evaluates on elements `x` of `L`
to the characteristic polynomial of `φ x` acting on `M`. -/
noncomputable def polyCharpoly : Polynomial (MvPolynomial ι R) :=
φ.polyCharpolyAux b (Module.Free.chooseBasis R M)
