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Stabilisation of gcf Computations Under Termination #

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Summary #

We show that the continuants and convergents of a gcf stabilise once the gcf terminates.

theorem generalized_continued_fraction.terminated_stable {K : Type u_1} {g : generalized_continued_fraction K} {n m : } (n_le_m : n m) (terminated_at_n : g.terminated_at n) :

If a gcf terminated at position n, it also terminated at m ≥ n.