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You can even generalize linear algebra algorithms to closed semirings and have some really cool algorithms pop out, like finding the shortest path in graphs. There's a great paper called "Fun with Semirings" that goes into more details; unfortunately looks like the PDF isn't easily available online any more, but I found some slides[1] that seem to cover the same ideas well enough.

[1]: https://pdfs.semanticscholar.org/2e43/477e26a54b2d1a046c2140...

Okay I went over the slides and good lord this would have made my life easier not too long ago.

This deserves its own HN post imho.

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