Chris Pressey
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 Mar24 awarded Nice Question Sep24 awarded Autobiographer Dec14 awarded Custodian Dec14 reviewed Reviewed cyclic vector exists for symmetric operator iff there no repeated eigenvalues Dec14 awarded Scholar Dec14 accepted Has this algebraic structure been named or studied? Dec12 comment The G.C.D of two numbers is $23$. The other two factors of the L.C.M are $13$ and $14$. I find the statement "The other two factors of the LCM are 13 and 14" somewhat confusing, as 14 is not prime. Why does it not say "The other factor is 182" or "The other prime factors are 13, 7, and 2"? I'm concerned that there might have been an error in transcription. Dec11 comment Has this algebraic structure been named or studied? True, Joy's quote does not work like that, but it's fairly easy to make a variation which does, and I was hoping that adding another property (however slight) might bring it closer to something algebraically conventional. Joy's quote is also intensional, whereas what I'm working with is extensional. I just realized that that means, in Joy, a=b does not imply [a]=[b]; but [a]=[b] still does imply a=b, and at any rate, extensionality is pretty important for my current purposes. Dec11 awarded Commentator Dec11 comment Has this algebraic structure been named or studied? That would work better, assuming I can find a suitable $c$. It is possible to transform programs in these languages in a way that removes brackets and adds a symbol which basically says "bracket this other thing"; that operator is a good candidate for this $c$. But there are issues with associativity that I don't know if I can get around, with that approach; it'll take some time for me to look into it. Dec11 comment Has this algebraic structure been named or studied? @Thomas, if you want to post that as an answer, I'll vote it up. Even knowing that it's not an endomorphism is helpful. In a sense, ^ imposes a hierarchical structure on the elements of S, which I think suggests that I should look into things like lattices instead. Dec10 revised Has this algebraic structure been named or studied? explicitly state non-idempotency of ^ Dec10 comment Has this algebraic structure been named or studied? The commutativity of + is not a good fit, but the idea of fixing a c like that is intriguing. Do you happen to know if there's a good example of using that technique in some other context? Dec10 revised Has this algebraic structure been named or studied? included the cancellative property of ^ and reformatted properties into bulleted lists Dec10 comment Has this algebraic structure been named or studied? @Thomas: a concrete example of the structure is: strings of symbols with brackets, with a semantics which gives the substrings inside brackets a different meaning. Joy is one such programming language based on this framework. The underlying monoid for Joy is well-described in that paper, but the bracketing operator (Joy's [...], my ^) is much less well-described algebraically, and I'm trying to find out more about where it might fit in (or be made to fit in.) Dec10 comment Has this algebraic structure been named or studied? @Thomas: Yes, ^a=^b implies a=b. But no, ^1≠1. I take it that, if ^1=1 held, it would be an endomorphism? Thanks to you and ineff for pointing this out -- it may be possible to reformulate things (in a contrived way) to get a special restricted case where ^1=1 and see where that leads me. Dec10 awarded Student Dec10 asked Has this algebraic structure been named or studied? Dec9 awarded Analytical Dec9 comment How can Busy beaver($10 \uparrow \uparrow 10$) have no provable upper bound? This makes sense, thanks. But I'm still a bit mystified about why $10\uparrow\uparrow 10$ was chosen as the stated bound -- you seem to agree that it is much larger than you would actually need. Is it just a case of being extremely conservative? (Is this worth asking in a separate question?)