00:16:22 <arseniiv> hello bye
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00:37:54 <ArthurStrong> Speaking of SAT solvers
00:38:00 <ArthurStrong> SAT solver on top of regex matcher https://yurichev.com/news/20200621_regex_SAT/
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00:44:24 <esowiki> [[BWTFN]] M https://esolangs.org/w/index.php?diff=74147&oldid=64508 * PythonshellDebugwindow * (+44) /* Print something 1000 times */
00:44:48 <esowiki> [[BWTFN]] M https://esolangs.org/w/index.php?diff=74148&oldid=74147 * PythonshellDebugwindow * (-4) Fix headers
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03:24:08 <esowiki> [[GORBITSA]] M https://esolangs.org/w/index.php?diff=74149&oldid=74144 * ZippyMagician * (+8) Fix interpreter error
03:34:32 <esowiki> [[Special:Log/newusers]] create  * Chibill *  New user account
03:37:28 <esowiki> [[Esolang:Introduce yourself]]  https://esolangs.org/w/index.php?diff=74150&oldid=74117 * Chibill * (+181) 
03:37:54 <esowiki> [[Esolang:Introduce yourself]]  https://esolangs.org/w/index.php?diff=74151&oldid=74150 * Chibill * (+1) 
03:42:55 <esowiki> [[GORBITSA]]  https://esolangs.org/w/index.php?diff=74152&oldid=74149 * Chibill * (+423) Add my GORBITSA compiler to the list of implementations.
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03:44:01 <esowiki> [[GORBITSA]]  https://esolangs.org/w/index.php?diff=74153&oldid=74152 * Chibill * (+14) Fix link to it.
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03:50:08 <esowiki> [[User:Arcorann]] N https://esolangs.org/w/index.php?oldid=74154 * Arcorann * (+38) Created page with "== Subpage index== *[[/TPK Algorithm]]"
04:30:21 <zzo38> Do you have a copy of the envelope for the IBM flowchart template?
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05:03:02 <ArthurStrong> zzo38: me?
05:04:07 <zzo38> Well, anyone, really.
05:07:25 <int-e> `? zzo38
05:07:28 <HackEso> zzo38 is not actually the next version of fungot, much as it may seem.
05:07:59 <ArthurStrong> `? int-e
05:08:00 <HackEso> int-e är inte svensk. Hen kommer att spränga solen. Hen står för sig själv. Hen gillar inte färger, men han gillar dissonans. Er hat ein Hipster-Spiel gekauft.
05:08:04 <ArthurStrong> `? ArthurStrong 
05:08:09 <HackEso> ArthurStrong ? ¯\(°​_o)/¯
05:08:20 <ArthurStrong> `? shachaf 
05:08:22 <HackEso> Queen Shachaf of the Dawn sprø som selleri and cosplays Nepeta Leijon on weekends. He hates bell peppers with a passion. He doesn't know when to stop asking questions. We don't like this.
05:09:27 <ArthurStrong> `? arseniiv
05:09:29 <HackEso> arseniiv is a blank slate who is afraid of alchemy, especially the kind involving chalk.
05:09:50 <ArthurStrong> what to do to earn a personal entry for this bot? wondering...
05:09:57 <ArthurStrong> `? shachaf 
05:09:58 <HackEso> Queen Shachaf of the Dawn sprø som selleri and cosplays Nepeta Leijon on weekends. He hates bell peppers with a passion. He doesn't know when to stop asking questions. We don't like this.
05:10:10 <shachaf> ?
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07:05:39 <esowiki> [[User:Arcorann/TPK Algorithm]] N https://esolangs.org/w/index.php?oldid=74155 * Arcorann * (+1637) Created page with "The '''TPK algorithm''' is an algorithm used by Luis Trabb Pardo and Donald Knuth in the 1977 paper "The Early Development of Programming Languages" to demonstrate various fea..."
07:06:09 <esowiki> [[DOGO]]  https://esolangs.org/w/index.php?diff=74156&oldid=70760 * Arcorann * (+35) /* External resources */
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08:31:16 <esowiki> [[Special:Log/newusers]] create  * Horsey *  New user account
09:07:27 <esowiki> [[Int**]] M https://esolangs.org/w/index.php?diff=74157&oldid=74113 * Hakerh400 * (+46) 
09:32:59 <esowiki> [[Esolang:Introduce yourself]]  https://esolangs.org/w/index.php?diff=74158&oldid=74151 * Georgelam6 * (+179) /* Introductions */
09:33:14 <esowiki> [[Bitshit]] N https://esolangs.org/w/index.php?oldid=74159 * Georgelam6 * (+1019) Bitshit is a programming language that can only work in bits.
09:34:17 <esowiki> [[Bitshit]]  https://esolangs.org/w/index.php?diff=74160&oldid=74159 * Georgelam6 * (+105) 
09:35:11 <esowiki> [[Bitshit]]  https://esolangs.org/w/index.php?diff=74161&oldid=74160 * Georgelam6 * (-98) 
09:35:37 <esowiki> [[Bitshit]]  https://esolangs.org/w/index.php?diff=74162&oldid=74161 * Georgelam6 * (+98) 
09:36:23 <esowiki> [[Bitshit]]  https://esolangs.org/w/index.php?diff=74163&oldid=74162 * Georgelam6 * (+48) 
09:37:29 <esowiki> [[Bitshit]]  https://esolangs.org/w/index.php?diff=74164&oldid=74163 * Georgelam6 * (+85) 
09:38:48 <esowiki> [[Bitshit]]  https://esolangs.org/w/index.php?diff=74165&oldid=74164 * Georgelam6 * (-40) 
09:40:16 <esowiki> [[Bitshit]]  https://esolangs.org/w/index.php?diff=74166&oldid=74165 * Georgelam6 * (-69) 
09:40:55 <esowiki> [[Bitshit]]  https://esolangs.org/w/index.php?diff=74167&oldid=74166 * Georgelam6 * (-113) 
09:42:20 <esowiki> [[Bitshit]]  https://esolangs.org/w/index.php?diff=74168&oldid=74167 * Georgelam6 * (+76) 
09:42:44 <esowiki> [[Bitshit]]  https://esolangs.org/w/index.php?diff=74169&oldid=74168 * Georgelam6 * (-4) 
09:50:43 <esowiki> [[Esolang:Introduce yourself]]  https://esolangs.org/w/index.php?diff=74170&oldid=74158 * Horsey * (+44) 
09:51:18 <esowiki> [[GORBITSA]]  https://esolangs.org/w/index.php?diff=74171&oldid=74153 * Horsey * (+1582) /* Programs */
09:51:51 <esowiki> [[GORBITSA]] M https://esolangs.org/w/index.php?diff=74172&oldid=74171 * Horsey * (+9) /* Snake (By Horsey) */
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10:10:26 <Dion> Hi! I had a question. If I, for example, wanted to add features to my language that i created and submitted a couple days ago, would it be better to just edit the existing page, make a 2.0 version of the language or just not do anything for now?
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10:27:30 <esowiki> [[MAWP]]  https://esolangs.org/w/index.php?diff=74173&oldid=74081 * Dion * (+27) 
10:39:32 <myname> edit it.
10:41:49 <myname> even _if_ you made a 2.0 version, why would you not put that on the same page?
10:45:28 <Dion> Ok, thx!
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11:28:25 <esowiki> [[GORBITSA]]  https://esolangs.org/w/index.php?diff=74174&oldid=74172 * Horsey * (+17) /* Snake (By Horsey) */
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11:51:44 <esowiki> [[GORBITSA]] M https://esolangs.org/w/index.php?diff=74175&oldid=74174 * Horsey * (+21) /* Snake (By Horsey) */
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12:22:36 <arseniiv> <ais523> that's what I get for not reading the whole scrollback before commenting  <b_jonas> yeah, I do that all the time too => I’ve read this part only now even
12:55:08 <esowiki> [[Bitshit]] M https://esolangs.org/w/index.php?diff=74176&oldid=74169 * PythonshellDebugwindow * (+250) wikify
12:55:20 <esowiki> [[Bitshit]] M https://esolangs.org/w/index.php?diff=74177&oldid=74176 * PythonshellDebugwindow * (+0) /* External resources */ fix cat
13:06:17 <esowiki> [[Con-Text]] M https://esolangs.org/w/index.php?diff=74178&oldid=12135 * PythonshellDebugwindow * (+207) /* Implementation */ cats + tc
13:06:26 <esowiki> [[Con-Text]] M https://esolangs.org/w/index.php?diff=74179&oldid=74178 * PythonshellDebugwindow * (+0) /* Turing-completeness */
13:21:17 <esowiki> [[Wumpus]] M https://esolangs.org/w/index.php?diff=74180&oldid=54081 * PythonshellDebugwindow * (+6) 
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13:45:58 <arseniiv> @ask cpressey in Tandem, should `lα → α` be considered changing stack `l`? I’d use a simple diff to determine if R & S = 0 and if R | S should raise an error when in deterministic mode, if `lα → α` and `lα… → α…` are identities, otherwise I’d need to collect changes when applying R*, to know all `l` for which there were changes, even if their final values ended up unchanged
13:45:58 <lambdabot> Consider it noted.
13:54:18 <esowiki> [[Arch]] M https://esolangs.org/w/index.php?diff=74181&oldid=67745 * PythonshellDebugwindow * (+3) /* Computational Properties */
13:56:36 <esowiki> [[An arch is simply a curve.]] M https://esolangs.org/w/index.php?diff=74182&oldid=68240 * PythonshellDebugwindow * (+1) /* Specification */
14:04:34 <arseniiv> @tell cpressey “and M(R) is the set of objects matched by the pattern at some given point in the rewrite process” => ah, this part seems to indicate that `lα → α` is not 1
14:04:34 <lambdabot> Consider it noted.
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14:20:29 <esowiki> [[Talk:Jumpmin]] N https://esolangs.org/w/index.php?oldid=74183 * Emerald * (+1145) /* Extra minimization */ new section
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14:45:55 <esowiki> [[GORBITSA]]  https://esolangs.org/w/index.php?diff=74184&oldid=74175 * ZippyMagician * (-59) Large bugfix of interpreter
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14:50:42 <esowiki> [[GORBITSA]]  https://esolangs.org/w/index.php?diff=74185&oldid=74184 * ZippyMagician * (+0) Update node.js interpreter
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15:39:02 <esowiki> [[Perl]] M https://esolangs.org/w/index.php?diff=74186&oldid=68956 * PythonshellDebugwindow * (+23) /* In shell scripts */ cat
15:43:03 <esowiki> [[NotBrainFuck]] M https://esolangs.org/w/index.php?diff=74187&oldid=66056 * PythonshellDebugwindow * (-16) unpipe
15:44:09 <zzo38> Would English spellings be less messy if you are using Germanic rather than Latin alphabets? Latin alphabets are good for Latin writing, but maybe not so much in English?
15:45:33 <esowiki> [[No]] M https://esolangs.org/w/index.php?diff=74188&oldid=70042 * PythonshellDebugwindow * (+88) /* Hello, World program */
15:45:52 <esowiki> [[No]] M https://esolangs.org/w/index.php?diff=74189&oldid=74188 * PythonshellDebugwindow * (+1) /* Hello, World program */
15:47:12 <esowiki> [[No]] M https://esolangs.org/w/index.php?diff=74190&oldid=74189 * PythonshellDebugwindow * (+158) cats + deadlink /* External resources */
15:47:14 <b_jonas> zzo38: I don't think any popular germanic language has an ortohgraphy that could reasonably get close to representing English's large inventory of vowel qualities
15:47:48 <esowiki> [[User:Dominic Zdan]] N https://esolangs.org/w/index.php?oldid=74191 * Dominic Zdan * (+168) Created page with "== What I do ==  I am a Ruby programmer  I am planning on creating my own esolang == What im working on ==  Im working on a language that has a self  explanatory syntax"
15:47:58 <b_jonas> so no
15:48:45 <zzo38> I mean using runes, not the modern alphabets
15:48:52 <esowiki> [[User:Dominic Zdan]]  https://esolangs.org/w/index.php?diff=74192&oldid=74191 * Dominic Zdan * (+3) /* What I do */
15:51:16 <esowiki> [[User:Dominic Zdan]]  https://esolangs.org/w/index.php?diff=74193&oldid=74192 * Dominic Zdan * (+18) 
15:51:34 <zzo38> I think the English runes are actually more than those of other Germanic languages
15:51:43 <esowiki> [[User:Dominic Zdan]]  https://esolangs.org/w/index.php?diff=74194&oldid=74193 * Dominic Zdan * (-8) /* What I do */
15:52:01 <esowiki> [[User:Dominic Zdan]]  https://esolangs.org/w/index.php?diff=74195&oldid=74194 * Dominic Zdan * (-6) /* What im working on */
15:57:52 <esowiki> [[User:Dominic Zdan]]  https://esolangs.org/w/index.php?diff=74196&oldid=74195 * Dominic Zdan * (+2) /* What im working on */
15:58:13 <esowiki> [[User:Dominic Zdan]]  https://esolangs.org/w/index.php?diff=74197&oldid=74196 * Dominic Zdan * (+0) /* What im working on */
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15:59:30 <esowiki> [[User:Dominic Zdan]]  https://esolangs.org/w/index.php?diff=74200&oldid=74199 * Dominic Zdan * (-1) /* What im working on */
16:00:05 <esowiki> [[User:Dominic Zdan]]  https://esolangs.org/w/index.php?diff=74201&oldid=74200 * Dominic Zdan * (-3) /* What im working on */
16:00:27 <esowiki> [[User:Dominic Zdan]]  https://esolangs.org/w/index.php?diff=74202&oldid=74201 * Dominic Zdan * (-5) /* What I do */
16:00:38 <esowiki> [[User:Dominic Zdan]]  https://esolangs.org/w/index.php?diff=74203&oldid=74202 * Dominic Zdan * (-3) /* What im working on */
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16:21:42 <esowiki> [[GORBITSA]]  https://esolangs.org/w/index.php?diff=74204&oldid=74185 * ZippyMagician * (+9) Update
16:24:27 <b_jonas> zzo38: the runes don't have more vowels either, I think
16:24:48 <b_jonas> at least as far as I know futhark runes
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18:34:47 <esowiki> [[Talk:Jumpmin]]  https://esolangs.org/w/index.php?diff=74205&oldid=74183 * Emerald * (+207) Edit
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19:36:22 <arseniiv> zzo38: IPA may be enough, and there were several other attempts to make an English-tailored phonetic alphabet for use in pre-school teaching and something like that, though all based on latin, enhanced with additional letters (almost just like in IPA, though maybe more kid-friendly and connected with the usual orthography). But the situation is bad as phonology is different in some details for various English dialects, even if we take only prestigious 
19:36:22 <arseniiv> ones. Though these differences are not that big yet, but they definitely would cause arguing which phonetic spelling is better. There are even minor disputes what phonemes there are for any given language variant as real languages are a little bit more complex than a simple (and for many purposes, good) model phonology uses
19:39:59 <zzo38> I know the phonology is different in different dialects, but I thought runes already solved that problem, although maybe I am wrong
19:49:31 <b_jonas> arseniiv: "based on latin" how much? which of these do you count as based on latin: Shavian, futhark, braille, Moon, American/German fingerspelling, British fingerspelling, semaphore flags, morse, Baudot code, Hollerith card code (or EBCDIC and MIX character code based on them), ASCII
19:50:10 <b_jonas> of those, only Shavian is a pronunciation-based system, the rest are just alternate scripts for that are sometimes used to write English with the same spelling system
19:51:21 <arseniiv> b_jonas: yeah I mainly considered phonetic scripts
19:52:37 <b_jonas> also I guess I should ask about the major stenographic systems used for English: Pittman and Gregg, since those definitely try to be somewhat pronunciation-based, do you count as based on Latin?
19:52:49 <arseniiv> zzo38: phonology is not that different usually, phonemes are more abstract than the sounds we speak, but “phonetical” writing usually describes something on phonemic level rather than something more lower-level
19:53:03 <arseniiv> which is unfortunate naming
19:53:27 <b_jonas> arseniiv: ok, but if you only consider phonetic scripts, then does Shavian and/or Deseret count as Latin-based?
19:54:24 <arseniiv> b_jonas: yeah I didn’t want to say they are all based on latin, sorry :D but people seem to concentrate on latin-based when making a graphics which is easier to transition into from the current one
19:58:19 <b_jonas> I know there are several phonetic notations for English that are clearly based on latin: several variants based on IPA, a few that try to be ASCII transcriptions of IPA-like systems, a few based on diacritics over letters in Webster dictionary's style, and a few others like the notation in http://www.wyrdplay.org/AlanBeale/CAAPR-ref.html (strongly recommended) and the notation in 
19:58:25 <b_jonas> http://www.speech.cs.cmu.edu/cgi-bin/cmudict (not recommended)
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20:06:06 <zzo38> For writing the pronounciation, I also had another idea rather than IPA, which is not based on Latin or other alphabets but rather based on the position in the consonants and vowels grid.
20:12:06 <esowiki> [[Blablafuck]] M https://esolangs.org/w/index.php?diff=74206&oldid=50847 * PythonshellDebugwindow * (+694) /* Hello World */
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20:19:21 <rain1> https://en.wikipedia.org/wiki/Lamplighter_group
20:19:53 <esowiki> [[Consequential]] M https://esolangs.org/w/index.php?diff=74207&oldid=68959 * PythonshellDebugwindow * (-2) 
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20:24:39 <arseniiv> do I need to compute something with all the 2^n conjugates of a number x ∈ Q[√a1][√a2]…[√an] to find its minimal polynomial over Q?
20:25:30 <rain1> you may not need to
20:26:13 <rain1> you can create a nxn matrix that represents the action of multiplication by x on a given basis, if you can find any basis for Q(x)
20:26:25 <rain1> then the characteristic polynomial of that matrix (M - Ix) will be the minpoly
20:29:03 <rain1> wait
20:29:09 <rain1> im not sure if it is nxn anymore
20:29:32 <rain1> maybe it's 2^n x 2^n i only did this with n=2 before
20:29:52 <arseniiv> rain1: oh! This seems both a more right way to do things and both a more intellectually demanding one (reading about finding a basis for Q(x)). Hm did you mean Q[x]? All a1, …, an are positive and don’t have a square root in the corresponding fields Q, Q[√a1], …, Q[√a1]…[√a(n−1)]
20:30:46 <rain1> let's think about the n=3 case, say sqrt(2), sqrt(3), sqrt(5)
20:30:52 <arseniiv> rain1: hm if the size is exponential then surely a plain multiplication of (X − x), (X − one conjugate of x), … (X − the last conjugate of x) will be the same complexity?
20:30:55 <rain1> yeah it has size 2^3 = 8...
20:30:57 <rain1> my bad
20:31:52 <rain1> I believe that a = sqrt(2) + sqrt(3) + sqrt(5), will be a primitive element so {1,a,a^2,a^3,a^4,...,a^7} will be a basis
20:32:19 <arseniiv> no problem. I started thinking about this problem by reading a Python impl of constructible numbers here: https://github.com/leovt/constructible/blob/master/constructible.py#L323 (it follows another impl in Haskell but that one doesn’t concerns itself with hashes and minimal polys)
20:32:30 <rain1> so it will not be too bad to produce the 2^n x 2^n matrix
20:33:00 <rain1> hm but the min poly is not enough 
20:33:19 <rain1> you also need an approximation of the value or something, to uniquely determine which root of the minpoly you are referring to?
20:33:54 <arseniiv> for the hash? why? If 2^n elements have the same hash and n is a reasonable value which won’t blow one’s RAM off, I think it should be cool
20:34:33 <arseniiv> (and the equality testing is covered without resorting to the hash; this one is easy)
20:34:39 <rain1> ah right!
20:35:02 <rain1> earlier I meant det(M - Ix)
20:36:19 <arseniiv> ah, yeah, I read that as “the characteristic polynomial of M” and negated that typo :D
20:38:59 <moony> ^help
20:38:59 <fungot> ^<lang> <code>; ^def <command> <lang> <code>; ^show [command]; lang=bf/ul, code=text/str:N; ^str 0-9 get/set/add [text]; ^style [style]; ^bool
20:39:05 <rain1> I guess the constrible numbers is the field with all square roots added(?)
20:39:13 <rain1> connstructable
20:39:32 <arseniiv> yeah
20:40:28 <arseniiv> it’s a union of all Q[√…]…finite…[√…]
20:41:24 <arseniiv> a union in a sensible manner, I don’t know how that’s done precisely but for any two elements you can find a Q[√…]…finite…[√…] they both immerse in
20:42:56 <b_jonas> arseniiv: it's done by making it a subfield of the field of complex numbers
20:43:45 <arseniiv> I worry current implementations don’t try to compress the count of field extensions too eagerly for it to be usable in actual computations, but I haven’t read their code (neither Python, nor Haskell) enough
20:44:13 <arseniiv> b_jonas: ah, that thing. Then the reals would be sufficient for the case used in geometry
20:44:27 <b_jonas> arseniiv: I think GAP's implementation handles that well, I don't know about other implementations
20:44:55 <rain1> or just all real square roots
20:45:08 <b_jonas> arseniiv: reals vs complexes doesn't matter much here on account that sqrt(-x) = i*sqrt(x), so the complex version is just the real version extended with i
20:45:30 <b_jonas> no wait, that's not enough proof
20:45:31 <arseniiv> agree
20:45:35 <arseniiv> oh
20:46:33 <arseniiv> at least I agree something like that should be going there, C being algebraically closed and all that
20:49:49 <rain1> i like also how the origami constructible numbers includes cube roots
20:50:25 <arseniiv> this is nice
20:50:37 <rain1> so you can trisect angles 
20:50:45 <rain1> I don't know how this relates to cube roots
20:50:48 <rain1> but i heard you can
20:54:37 <b_jonas> yes, the point is that you can write the square root of a complext number as sqrt(x + i*y) = sqrt((sqrt(x**2+y**2) + x)/2) + i*sqrt((sqrt(x**2+y**2+y)/2), which is not an equation I know by heart but I probably should, but I do know that it exists,
20:54:56 <rain1> you don't need to know it
20:55:08 <rain1> I didn't know this
20:55:47 <b_jonas> and beacuse of that, if you want to do calculations on complex numbers with square roots and field ops, you can emulate them with square roots and field ops on real numbers,
20:56:34 <b_jonas> which is the same as doing compass and ruler constructions, so you don't get more constructible numbers on complexes, or more square root field extensions if you allow complex square roots;
20:57:16 <b_jonas> but this case contrasts to cube roots, where you definitely can't compute the cube root of a complex number using just real cube roots, real square roots, and field operations and i
20:57:16 <arseniiv> oh I think I nailed the algorithm to compute a minpoly
20:57:26 <rain1> noice
20:57:28 <rain1> how did you do it?
20:58:17 <b_jonas> which is why you can't solve some cubic equations with real coeffs using only real cube roots, but you can solve them using complex square roots.
20:58:34 <rain1> woah
20:59:06 <b_jonas> That's not really why you can't construct angle trisections: you can't construct either kind of cube root with a compass, you can't even construct 2**(1/3) with a compass
20:59:35 <b_jonas> although you would need a complex cube root for angle trisection.
21:00:40 <arseniiv> rain1: the conjugation on each level of the Q[...]... tower has usual complex conjugation properties like (xy)′ = x′y′, (x + y)′ = x′ + y′, 0′ = 0, 1′ = 1 so we can conjugate polynomials coefficientwise and get polynomials for larger and larger products of monomials each for its own conjugate of the number
21:00:48 <b_jonas> note that in the above formula, if x and y are real, all four square roots have nonnegative real numbers as the argument
21:00:58 <b_jonas> arseniiv: does that make sense?
21:02:48 <arseniiv> for example we start with P0 ≡ X − x, then let’s denote more and more deep conjugations as ′, ″, ‴, …, then (X − x) (X − x′) is the same as (X − x) (X − x)′ = P0 P0′ =: P1, then we do P1 P1′ =: P2 and so on for each field extension right to the inner Q then we’re done
21:03:06 <arseniiv> I don’t know how bad it is but seems pretty economical
21:03:22 <rain1> oh yeah i see
21:03:34 <rain1> but this would require lots of multiplications in the base field
21:03:49 <rain1> it will work though
21:04:00 <arseniiv> ah but there’s a little caveat, we need to skip “inessential extensions” which give the same P
21:04:23 <esowiki> [[User:Dominic Zdan]]  https://esolangs.org/w/index.php?diff=74208&oldid=74203 * Dominic Zdan * (+57) /* What im working on */
21:04:33 <b_jonas> arseniiv: there's actually an algorithm to do computations on constructible numbers using nothing but fancy square root stuff, no fancy field theory tricks, but in general it's so slow that it's impractical, which is why you want an implementation like that in GAP (which actually handles a much larger subset of algebraic numbers than constructible numbers)
21:04:44 <arseniiv> I mean, if Pi′ = Pi, then we set P(i+1) := Pi, not a square
21:05:41 <arseniiv> b_jonas: do you mean something better than 2^n rational numbers for each Q[√a1]…[√an]?
21:06:23 <b_jonas> arseniiv: the former isn't much better than that (you can use a sparse vector), I don't know how the latter works
21:07:00 <b_jonas> you can look it up in the docs
21:07:08 <arseniiv> maybe the latter uses something about modules and things like Gröbner bases or what was it
21:07:34 <rain1> you can work in the ring Q[x,y,z]/(x^2-2,y^2-3,z^2-5)
21:07:49 <rain1> field
21:08:18 <b_jonas> I know there's also an algorithm to compute with arbitrary algebraic complex numbers, but it's so difficult that I know of only one thing that implements it, and that thing is Mathematica and its implementation is effectively a black-box. I have no idea how that algorithm works.
21:08:44 <b_jonas> arseniiv: the GAP docs has a description, if you can't find it ping me and I'll look up a link
21:09:05 <b_jonas> plus it's open source
21:09:16 <arseniiv> <b_jonas> arseniiv: does that make sense? => I certainly remember finding a formula for sqrt(x + iy) but I don’t remember if that ended up as your one sorry
21:09:26 <rain1> I always thought that would be a good project to do, exact algebraic computations
21:09:37 <rain1> I think that a pair of approximation + minpoly would be OK
21:09:54 <rain1> since an approximation is enough to let you compute a more accurate approximation
21:10:24 <arseniiv> hm that one was reminiscent of half-sine and half-cosine formulas I think (for obvious reasons of course) but I think it would need some cooking to turn into this one
21:10:31 <rain1> i'm not exactly sure how you + and * these elements
21:10:55 <arseniiv> <b_jonas> arseniiv: the GAP docs has a description, if you can't find it ping me and I'll look up a link => thanks! Though I’m not pursuing this think that hard yet
21:10:57 <b_jonas> never mind, I'll look it up: https://www.gap-system.org/Manuals/doc/ref/chap18.html
21:10:59 <rain1> but it would be very cool to do this exact computation with algebraic numbers
21:11:50 <rain1> perhaps the LLL algorithm would be fine
21:12:00 <rain1> you would just need a way to know how accurate an approximation is needed
21:12:05 <b_jonas> arseniiv: yes, it's not trivial that the algebraic numbers even form a field
21:12:13 <b_jonas> that's why you need minimal polynomials
21:12:27 <arseniiv> <b_jonas> never mind, I'll look it up: https://www.gap-system.org/Manuals/doc/ref/chap18.html => how does one represent those extensions via cyclotomic numbers?
21:12:54 <rain1> I may implement this
21:13:05 <rain1> are there some cool uses of it I could do if i make this?
21:13:13 <b_jonas> though for just constructible numbers, it is trivial that they form a field, that's basically how they're defined
21:14:23 <rain1> i have a bunch of math stuf i want to implement actually
21:14:26 <rain1> symmetric polys
21:14:44 <arseniiv> <rain1> are there some cool uses of it I could do if i make this? => precisely checking if tiles of some constructible (or algebraic) tileset match and constructing pieces of tesselations this way
21:15:10 <arseniiv> I saw into the constructible numbers once because of precisely this
21:15:53 <arseniiv> now I intend to use floating point and correct inaccuracies in some unknown manner but it should be possible as the construction is rigid
21:16:43 <rain1> oh yes
21:16:50 <b_jonas> arseniiv: I might be wrong here, but I think cyclotomic numbers are closed to field ops and square root, so any constructible number is a cyclotomic number. for representing a specific field extension, I don't know, you probably want a finite basis (a set of cyclotomics that generate your field), except this time you represent those numbers as cyclotomics
21:17:01 <rain1> there was also CReal which was very cool
21:17:15 <b_jonas> and do the field operations and square root on numbers represented as cyclotomics
21:17:31 <rain1> every abelian extension is a subfield of a cyclotomic field I think
21:17:46 <arseniiv> rain1: I implemented quaternionic logarithm once though I don’t think I know what branch that code selects; at least exponentiating it should give back the original number, modulo rounding errors
21:18:11 <arseniiv> it’s a pity I hadn’t found formulas anywhere, they’re quite simple
21:18:36 <arseniiv> and the result for a rotation quaternion is its axis-angle representation
21:19:45 <b_jonas> arseniiv: that's easy, you can implement it based on complex logarithm, because any non-real quaternion generates (as a real vector space) a set isomorphic (as a field) to complex numbers, and you can just construct the isomorphism with complex numbers trivially and compute logarithm there
21:19:50 <arseniiv> all the possible values of the logarithm in that case would just have the same axis and the angle + 2 π Z, as is indeed logical
21:20:23 <rain1> arseniiv, what would be an example of these algebraic tilings?
21:20:57 <rain1> https://blogs.ams.org/visualinsight/2013/09/01/algebraic-numbers/
21:21:25 <arseniiv> b_jonas: hm I didn’t thought about this that way but yeah I used that the vector quaternion squares to −1
21:21:39 <b_jonas> in practice this means you split your argument to its real part p and imaginary part q, compute r the mangitude of q, compute u + i*v = log(p + i*r), then log(p + q) = u + q/r*v
21:22:43 <arseniiv> rain1: I mean, if there is a tiling which uses regular heptagons, as they aren’t constructible, so one will indeed need arbitrary algebraic numbers to represent tilings with tiles like that
21:22:59 <rain1> interesting
21:23:55 <rain1> https://blogs.ams.org/visualinsight/2014/11/15/packing-regular-heptagons/
21:25:39 <arseniiv> rain1: oh, so one can use only two kinds of tiles, that kite-like one added
21:25:44 <b_jonas> arseniiv: but there's no such tiling, at least not in the Eucleadian plane. there is a hyperbolic tiling of course.
21:26:02 <arseniiv> that would be a nice test, to construct a piece of this packing, for the framework
21:26:21 <arseniiv> b_jonas: I mean not by only heptagons :D
21:27:06 <arseniiv> I quite like tilings with many kinds of tiles, compared to regular ones, they are boring
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21:27:31 <arseniiv> (the regular ones are boring; I need to use commas the right way)
21:27:46 <arseniiv> I’ll go to, I think
21:29:07 <b_jonas> arseniiv: well ok, at least there's no tiling with regular heptagons and other regular polygons either
21:30:19 <b_jonas> and if you just want something like a regular heptagon plus two tight packaging thingies on its side that complete it to a square, then the algebraic numbers in your heptagon don't actually cause any difficulties
21:31:13 <esowiki> [[Special:Log/newusers]] create  * AdCharity *  New user account
21:32:18 <arseniiv> <b_jonas> arseniiv: well ok, at least there's no tiling with regular heptagons and other regular polygons either => do you mean other than 3, 4 and 6-gon?
21:32:37 <esowiki> [[Esolang:Introduce yourself]]  https://esolangs.org/w/index.php?diff=74209&oldid=74170 * AdCharity * (+185) I added my name :P
21:32:49 <b_jonas> arseniiv: no, any that uses at least one regular heptagon
21:33:01 <arseniiv> <b_jonas> and if you just want something like a regular heptagon plus two tight packaging thingies on its side that complete it to a square, then the algebraic numbers in your heptagon don't actually cause any difficulties => yeah that tiling is not good enough
21:33:10 <b_jonas> because you can't even complete the surrounding of a vertex to 2 pi angle if there's a heptagon plus regular polygon angles
21:33:29 <arseniiv> b_jonas: ah now I think I parsed that
21:34:18 <arseniiv> the good kind of tiling is something like these:  https://en.wikipedia.org/wiki/Voderberg_tiling  https://en.wikipedia.org/wiki/Ammann%E2%80%93Beenker_tiling
21:35:02 <arseniiv> bye!
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21:52:05 <esowiki> [[User:Dominic Zdan]]  https://esolangs.org/w/index.php?diff=74210&oldid=74208 * Dominic Zdan * (-144) /* What im working on */
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