[Merged by Bors] - feat(continued_fractions) add equivalence of convergents computations #2459
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urkud
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Co-Authored-By: Bryan Gin-ge Chen <bryangingechen@gmail.com>
Thanks! Sorry for the typos D: I should get a spellchecker. |
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The Lean looks great (as you can see, I only have minor formatting comments).
What would be extremely helpful, I think, would be to have a sketch of the proof at the beginning of the file, in informal math talk and without details or computations (but pointers to the relevant lemmas in the file), and maybe also recall what the two definitions of convergents and convergents' are, to help the reader understand where the file is going.
From a math point of view, I would probably have done things using a formalism based on matrix products and homographies instead of the more elementary point of view that you develop, but in the end it is also nice like this.
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Also, you should change the header text of the PR to reflect the changes you have made (for instance, you have removed |
Co-Authored-By: sgouezel <sebastien.gouezel@univ-rennes1.fr>
Also fixed this. Thanks for the kind and detailled review :) |
Co-Authored-By: Bryan Gin-ge Chen <bryangingechen@gmail.com>
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bors r+ |
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Apr 25, 2020
…#2459) ### What Add lemmas showing that the two methods for computing the convergents of a continued fraction (recurrence relation vs direct evaluation) coincide. A high-level overview on how the proof works is given in the header of the file. ### Why One wants to be able to relate both computations. The recurrence relation can be faster to compute, the direct evaluation is more intuitive and might be easier for some proofs. ### How The proof of the equivalence is by induction. To make the induction work, one needs to "squash" a sequence into a shorter one while maintaining the value of the convergents computations. Most lemmas in this commit deal with this squashing operation. Co-authored-by: Kevin Kappelmann <kappelmann@users.noreply.github.com>
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Pull request successfully merged into master. Build succeeded: |
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…leanprover-community#2459) ### What Add lemmas showing that the two methods for computing the convergents of a continued fraction (recurrence relation vs direct evaluation) coincide. A high-level overview on how the proof works is given in the header of the file. ### Why One wants to be able to relate both computations. The recurrence relation can be faster to compute, the direct evaluation is more intuitive and might be easier for some proofs. ### How The proof of the equivalence is by induction. To make the induction work, one needs to "squash" a sequence into a shorter one while maintaining the value of the convergents computations. Most lemmas in this commit deal with this squashing operation. Co-authored-by: Kevin Kappelmann <kappelmann@users.noreply.github.com>
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May 16, 2020
…leanprover-community#2459) ### What Add lemmas showing that the two methods for computing the convergents of a continued fraction (recurrence relation vs direct evaluation) coincide. A high-level overview on how the proof works is given in the header of the file. ### Why One wants to be able to relate both computations. The recurrence relation can be faster to compute, the direct evaluation is more intuitive and might be easier for some proofs. ### How The proof of the equivalence is by induction. To make the induction work, one needs to "squash" a sequence into a shorter one while maintaining the value of the convergents computations. Most lemmas in this commit deal with this squashing operation. Co-authored-by: Kevin Kappelmann <kappelmann@users.noreply.github.com>
cipher1024
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Mar 15, 2022
…leanprover-community#2459) ### What Add lemmas showing that the two methods for computing the convergents of a continued fraction (recurrence relation vs direct evaluation) coincide. A high-level overview on how the proof works is given in the header of the file. ### Why One wants to be able to relate both computations. The recurrence relation can be faster to compute, the direct evaluation is more intuitive and might be easier for some proofs. ### How The proof of the equivalence is by induction. To make the induction work, one needs to "squash" a sequence into a shorter one while maintaining the value of the convergents computations. Most lemmas in this commit deal with this squashing operation. Co-authored-by: Kevin Kappelmann <kappelmann@users.noreply.github.com>
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What
Add lemmas showing that the two methods for computing the convergents of a continued fraction (recurrence relation vs direct evaluation) coincide. A high-level overview on how the proof works is given in the header of the file.
Why
One wants to be able to relate both computations. The recurrence relation can be faster to compute, the direct evaluation is more intuitive and might be easier for some proofs.
How
The proof of the equivalence is by induction. To make the induction work, one needs to "squash" a sequence into a shorter one while maintaining the value of the convergents computations. Most lemmas in this commit deal with this squashing operation.
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