num_den_reduced — Mathlib

English

As above, the discriminant after localization equals the localized discriminant.

Русский

Как выше, дискриминант после локализации равен локализованному дискриминанту.

LaTeX

$$$\\operatorname{discr}_{R_m}(\\mathrm{localization\\_basis}) = (\\mathrm{algebraMap}_R^{R_m})(\\operatorname{discr}_R(\\text{basis}))$$$

Lean4

theorem num_den_reduced (x : K) : IsRelPrime (num A x) (den A x) :=
  (Classical.choose_spec (Classical.choose_spec (exists_reduced_fraction A x))).1
    -- `@[simp]` normal form is called `mk'_num_den'`.

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