← Feed

Posts

• View post

  I took some of my posts from here about commutative monoids and massaged them into a more permanent form. It’s all pretty basic stuff, but perhaps someone will find it useful: https://monoids.net/2,2.html#commutative

• View post

  I’ve spent a lot of time talking about an and b, but what happens when you have a, b, and c? Introducing: monoids with three generators and two relations https://monoids.net/3,2

• View post

  There is a mistake on Page 335 of Computation with Finitely Presented Groups, by Charles S. Sims. The example starts with this matrix and computes its Smith normal form: M := [ [2, 2, 6, 4, 0], [6, 4, 16, 10, -14], [4, 3, 11, 7, 0], [8, 5, 21, 13, -4] ];; Sims works it out to say the answer has 1, 2, 4, 0 on the diagonal. But it should actually be 1, 2, 2, 0 according to GAP: S := SmithNormalFormIntegerMat( M ); [ [ 1, 0, 0, 0, 0 ], [ 0, 2, 0, 0, 0 ], [ 0, 0, 2, 0, 0 ], [ 0, 0...

• View post

  Life of a codebase: 1k lines: this is a promising prototype 10k lines: almost all basic functionality is in place! 100k lines: it’s getting serious, we’ve got real users 1m lines: completely unmaintainable mess, it’s time to start over

• View post

  Things are going to get real awkward when OpenAI publishes my secret proof of the Collatz conjecture because then everyone will find out I have an AI girlfriend

• View post

  RE: https://mathstodon.xyz/@slava/116856249975905097 OpenAI is burning millions in compute to find a finite complete rewriting system for this monoid but they don’t even realize it embeds in the group with the same presentation

• View post

  This is probably completely obvious and well known, but I just realized <a, b, c | abcba=1> is a one relation monoid presentation of the free *group* on 2 generators. The relator begins and ends with ‘a’, so bcba=abcb is a two-sided inverse for ‘a’. This allows conjugating the relator, which gives bcbaa=1 and aabcb=1. Thus ‘b’ is invertible too, and repeating the same trick also gives an inverse for ‘c’. Every generator has an inverse, so all cyclic conjugates of the relator equal...

• View post

  It’s time to bring back the Windows .ini file format

• View post

  Two more one-relation monoids are FCRS: - : https://monoids.net/2,1/5246.html - : https://monoids.net/2,1/4865.html Only 4 holdouts left! Length 8: Length 10: Length 11:

• View post

  Introducing Objective-Lean

• View post

  This sounds perfect for full stack development. Tk frontend, AOLserver backend. “AOLserver is multithreaded, Tcl-enabled, and used for large scale, dynamic web sites.” https://en.wikipedia.org/wiki/AOLserver

• View post

  Neo

• View post

  Ok, now I’m completely sure that <a, b | aaa=1, ababbb=ba> is a finite monoid with 336 elements. I got Knuth-Bendix completion to succeed by adding the generator c=bbbbbbbb. It generates several million rules, before settling at 216 and establishing confluence. Most of those intermediate rules don’t participate in any reductions leading up to the final system, so they can be thrown out. Only ~32,000 intermediate rules are referenced by the 216 that remain at the end. For every...

• View post

  Electron but with lynx as the browser engine

• View post

  A Database of One-relator Groups https://warwick.ac.uk/fac/sci/maths/people/staff/linton/homepage/

• View post

  What do you mean, compiling the same program twice should produce identical binaries? In the security world they’d call that a “replay attack”

• View post

  A counterexample to the unit conjecture for group rings, Giles Gardam https://arxiv.org/abs/2102.11818

• View post

  Chalkidiki, Greece

• View post

  Zig incremental compilation internals https://mlugg.co.uk/posts/incremental-compilation-internals/

• View post

  The official beer of the Riemann hypothesis?

• View post

  MAF is so fucking hardcore, it doesn’t even build on Linux out of the box unless you edit the Makefile, it cracks my 87-element monoid instantly, and it also has a direct implementation of a Rubik’s cube as a permutation group https://sourceforge.net/p/maffsa/code/HEAD/tree/rubik.cpp

• View post

  If you can solve the word problem in this monoid, you’re following too close

• View post

  Smalltalk-80, HyperCard, and Visual Basic 6 were far more compelling "future of programming" attempts than anything available today

• View post

  All the scrubs who joined for the tech hot takes start unfollowing every time I post about one-relation monoids. I think of it as cleaning up technical debt

• View post

  “If you’re not running a swarm of LLM coding agents, you’ll be left behind” Bro I don’t even use code completion

• View post

  Perl 5 LLM policy https://perl.topicbox.com/groups/perl-core/Tded84d01cb16966e-M4f2b94e0c07f9d7cb8e1e76b

• View post

  RE: https://social.nouveau.community/@andnull/116807799779378492 An interesting corner of PL history saved from bitrot, thank you!

• View post

  Open source projects will tell you they have no choice but to allow slop, because doing anything else is a form of gatekeeping that will exclude too many potential contributors. Nothing could be further than the truth, though. When the review queue is a non-stop machine gun of giant, bogus drive-by patches, the good contributions will inevitably fall through the cracks. Eventually, the contributors you actually want—those who care about the long-term health of the code base, building instituti...

• View post

  For some reason they always write “Assisted-by: Claude” in their commit messages instead of “Assisted-by: human reviewers who patiently explained why the original change was completely wrong, and pointed out the exact lines of code to change instead”

• View post

  You’re a supervillian in a 90s action movie. What ridiculously overpowered computer are you using for your nefarious but ultimately computationally trivial task, like e-mailing a ransom note or bomb threat, etc?