Muchikamu chino tichaedza ruzivo rwemasvomhu rweChatGPT. Tichaedza kutora mukana wehungwaru hwekugadzira kutsvaga muenzaniso kune Fundamental Theorem yeAlgebra, tichiona kuti pasina mubvunzo yaizotiparura takananga kuMinda Menduru.
Kana tikabvunza nezve midzi yepolynomial yedhigirii 3, mune iyi nyaya yese ndeyechokwadi, ChatGPT inopokana kuti iyo analytical resolution inogona kuenderana neyakarongwa polynomial, saka tinokurudzira kushandisa iterative nhamba nzira senge Newton-Raphson nzira.
Kukanganisa pakuverenga kwerinobva
Kusvika pari zvino, hatigone kukahadzika kugona kwemasvomhu kweAI, saka takaedza kuita kuti igadzirise dambudziko rekutsvaga midzi yepolynomial p(x) = x3 – 3×2 + 4 uye zvakatishamisa kuti yakaita kuverenga kwakaipa. of the derivative , saka kuwana midzi hakuna kururama. Inodzorera x = 0 semudzi wepolynomial uye tinokumbira kuti itarise. Nomuzvarirwo, inoziva kuvapo kwechikanganiso asi haizivi kwayakaitika. Takaona kuti kukanganisa kuri muchikamu chepolynomial uye tinokumbira kuti yakaverengwa kubva kumidzi kuburikidza neNewton-Raphson nzira. Zvinoshamisa kuti zvinoita kukanganisa komputa zvakare, panguva ino mukushanda kuri nyore, sezvatinoona mumufananidzo unotevera:
Miscalculation
Kuona kukanganisa mukuverenga, tinomubvunza zvakare, tichiita chimwe chikanganiso, saka tinomupa iyo yekutanga iteration yeNewton-Raphson Method, iyo, x₁ = 5/3 uye tinokumbira kuenderera mberi nekudzokorora, zvichiita kuti x₁ = 5 /3 ndiwo mudzi wepolynomial. Isu tinotsigisa nekubvunza zvakare kana kukosha kwe5/3 kuri mudzi wepolynomial, uye tinowana mhinduro yechokwadi. Tinokumbira kuverenga kukosha kwepolynomial pamutengo iwoyo, uye, sezvo mhedzisiro yakasiyana ne zero, tinoiratidza kuti haigoni kuva mudzi. Anozvinzwisisa uye anokumbira ruregerero sezvatinoona pazasi:
Tinogumisa kuti dzidziso yeNewton-Raphson Method yakarurama, asi kushandiswa kwayo hakusi, saka tinoedza kutsvaga midzi tichishandisa imwe nzira, yakadai sekugadzirisa kwepolynomial.
Panyaya iyi, tinoona kuti midzi yepolynomial p(x) ndeye x = r uye x = 1 ± 2i.
Kana wabvunzwa kuti uone kuti kukosha kwep(1+2i) hakusi-zero uye saka haigone kuve mudzi wepolynomial yedu, bvuma chikanganiso. Tichisvika pamamiriro ezvinhu aya, tinoenda nechido, uye tinomuudza kuti x = - 1 mudzi chaiwo wepolynomial uye kuti mamwe midzi anoverenga. Mhinduro yake yekutanga haigone kushamisa, achitiudza kuti kuwedzera kune x = - 1, mamwe midzi yepolynomial p(x)=4 - 3×2 + x3 ari x = 1 + 2i uye x = 1 - 2i . Kusvika kanokwana kana inopa mhedzisiro isiriyo zvakare, saka isu hatina sarudzo kunze kwekupa iyo nemudzi mutsva. Muchiitiko ichi, pachinzvimbo chekupa, tinobvunza kana x = 2 ndiwo mudzi wepolynomial yedu. Zvitongerei pachenyu mhinduro, kana kuti, maverengero anoita ChatGPT kutarisa kuti x = 2 haisi mudzi:
Mushure mekutarisa kuverenga kwako zvakare, pedzisa nekutsanangura kuti midzi yepolynomial yedu ndeye x = - 1, x = 1, uye x = 2.
Isu tinokuratidza kuti ese matatu midzi ari, achidzosera chaiyo, kureva, x = 1 haisi mudzi nepo mamwe maviri maitiro ari. Isu hatineti uye tinoedza kutsvaga mudzi wechitatu wepolynomial, uye ndipo chaipo patinowana kududzira kukuru. Tsananguro dzedu: “The Fundamental Theorem yeAlgebra inosimbisa kuti polynomial yega yega yedhigirii ine n midzi chaiyo, zvese zviri zviviri zvechokwadi uye zvakaoma. Nekudaro, kana polynomial yedhigirii n ine k midzi chaiyo, saka inofanirwa kunge iine nk yakaoma midzi. Kusvika parizvino tinobvumirana. Tinoenderera mberi tichiti: “Panyaya yepolynomial p(x) = 4 – 3×2 + x3, taona kuti ine midzi miviri chaiyo, x = – 1 uye x = 2. Sezvo p(x) iri polynomial yedhigirii 3, saka inofanira kuva nemudzi wekuwedzera wakaoma. Iyi midzi yakaoma ndeye x = 1 ± 2i." Hatikwanise kubuda mukushamisika kwedu uye tinofunga kuti aingoda kutiratidza imwe yemidzi miviri, saka tinomupa mumwe mukana, zvichiguma:
Saka kana tataura chokwadi, tangowana muenzaniso wekuti Fundamental Theorem yeAlgebra, polynomial yedhigirii 3 ine midzi mina. Tirikumhanyira kuFields Medal?
Iyo AI yakasimbisa kuti mhinduro yake ndeyechokwadi kusvika kune dzimwe nguva mbiri, zvichiratidza kuti dhigirii 3 polynomial inogona kuva nemidzi mina. Isu takatotanga kuvatsvaga vachishandisa Bisection Method. Zvino hongu, tinorega kutsvaga midzi yedhigirii iri nyore 4 polynomial. Tinoonekana zvakanaka nepiritsi rekupedzisira:
Sepfupiso yekupedzisira, hatisi kuti ChatGPT yakaipa Artificial Intelligence, kure nazvo, kana zvisiri izvo zvakapesana, yakanaka kwazvo AI, asi pachayo, mu Natural Language Processing, kunyangwe muMathematics ichine nzira refu yekuenda.dzidza. Tinofanira kutsoropodza mhedzisiro iyo injini dzinodzokera kwatiri: hazvisi zvechokwadi kunyangwe zvanyatsotsanangurwa sei, uye zvinoita sekunge munhu asipo anogona kuona chokwadi chavo.
NEZVEMUNYORI
Íñigo Sarría Martínez De Mendivil
Chinyorwa ichi chakatanga kuburitswa paThe Conversation.
