Path: ...!news.nobody.at!news.mb-net.net!open-news-network.org!news.gegeweb.eu!gegeweb.org!pasdenom.info!from-devjntp Message-ID: JNTP-Route: nemoweb.net JNTP-DataType: Article Subject: Re: Equation complexe References: <3DiHhMpGKZm9XLyE2e9bwKMlyDo@jntp> <9l0W7Z_B53Q745nmuJQl5m09fJQ@jntp> Newsgroups: sci.math JNTP-HashClient: EiLjgwup2zm_gfu3cxpVM-MU1YM JNTP-ThreadID: O5CXkAcAe1D7_dx2s1eq7KbScfI JNTP-ReferenceUserID: 4@nemoweb.net JNTP-Uri: https://www.nemoweb.net/?DataID=VMFIilIzgkSEOgy4b8XVfnxCsLc@jntp User-Agent: Nemo/1.0 JNTP-OriginServer: nemoweb.net Date: Wed, 26 Feb 25 19:18:28 +0000 Organization: Nemoweb JNTP-Browser: Mozilla/5.0 (X11; Linux x86_64; rv:109.0) Gecko/20100101 Firefox/115.0 Injection-Info: nemoweb.net; posting-host="88d8e3fc77776d6bcc186faa1aefc7625bd3eae9"; logging-data="2025-02-26T19:18:28Z/9223160"; posting-account="190@nemoweb.net"; mail-complaints-to="julien.arlandis@gmail.com" JNTP-ProtocolVersion: 0.21.1 JNTP-Server: PhpNemoServer/0.94.5 MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit X-JNTP-JsonNewsGateway: 0.96 From: Python Bytes: 2376 Lines: 26 Le 26/02/2025 à 20:13, Richard Hachel a écrit : > Le 26/02/2025 à 19:56, Python a écrit : >> Le 26/02/2025 à 19:50, Richard Hachel a écrit : >>> Le 26/02/2025 à 19:23, Python a écrit : >>> >>>> i is the equivalence class of the polynomial X in the quotient ring [actually a >>>> field] R[X]/(X^1+1). >> >>>> From that you can deduce that i^2 = -1. >>> >>> Yes. >> >> Well... Could you show it? I can. > > Can you show what i is the equivalence class of the polynomial X in the quotient > ring [actually a field] R[X]/(X^4+1)? This is a *definition* and definitely NOT you lie about "posing than i^2 = -1 as a definition". The point is to show that this definition is consistent (it is) and to show that, then, i^2 = -1. Again: you wrote "Yes". So can you show it? Or will you chicken out as usual?