[Merged by Bors] - refactor(Mathlib/Algebra/ContinuedFractions/*): generalize determinant formula for continued fraction computation to simple continued fraction #13555
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…simple continued fraction
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…t formula for continued fraction computation to simple continued fraction (#13555) Determinant formula for continued fractions in Mathlib is specialized for continued fraction computation: ```lean theorem GenContFract.determinant (not_terminated_at_n : ¬(of v).TerminatedAt n) : (of v).numerators n * (of v).denominators (n + 1) - (of v).denominators n * (of v).numerators (n + 1) = (-1) ^ (n + 1) := determinant_aux <| Or.inr <| not_terminated_at_n ``` This formula can be generalized for arbitrary simple continued fractions, so we generalize: ```lean theorem SimpContFract.determinant (not_terminatedAt_n : ¬(↑s : GenContFract K).TerminatedAt n) : (↑s : GenContFract K).nums n * (↑s : GenContFract K).dens (n + 1) - (↑s : GenContFract K).dens n * (↑s : GenContFract K).nums (n + 1) = (-1) ^ (n + 1) ``` Also, this PR renames `Real.exists_genContFract_convs_eq_rat` to `Real.exists_convs_eq_rat` which is forgotten to rename in #13210.
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Is there a reason we didn't add a deprecated alias for the renamed lemma? |
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Determinant formula for continued fractions in Mathlib is specialized for continued fraction computation:
This formula can be generalized for arbitrary simple continued fractions, so we generalize:
Also, this PR renames
Real.exists_genContFract_convs_eq_rattoReal.exists_convs_eq_ratwhich is forgotten to rename in #13210.This PR consists Continued fractions makes an isomorphism between irrationals and baire space
project