{"height":"190","url":"https://randommemory.hatenablog.com/entry/2016/08/27/152054","author_url":"https://blog.hatena.ne.jp/derwind/","provider_name":"Hatena Blog","title":"\u98fd\u304d\u305f\u3089\u3084\u3081\u3088\u3046Galois\u7406\u8ad6(17)\u2015\u6709\u9650\u4f53\u3067\u904a\u3076","version":"1.0","type":"rich","author_name":"derwind","blog_url":"https://randommemory.hatenablog.com/","width":"100%","published":"2016-08-27 15:20:54","provider_url":"https://hatena.blog","blog_title":"\u3089\u3093\u3060\u3080\u306a\u8a18\u61b6","image_url":null,"html":"<iframe src=\"https://hatenablog-parts.com/embed?url=https%3A%2F%2Frandommemory.hatenablog.com%2Fentry%2F2016%2F08%2F27%2F152054\" title=\"\u98fd\u304d\u305f\u3089\u3084\u3081\u3088\u3046Galois\u7406\u8ad6(17)\u2015\u6709\u9650\u4f53\u3067\u904a\u3076 - \u3089\u3093\u3060\u3080\u306a\u8a18\u61b6\" class=\"embed-card embed-blogcard\" scrolling=\"no\" frameborder=\"0\" style=\"display: block; width: 100%; height: 190px; max-width: 500px; margin: 10px 0px;\"></iframe>","categories":["math-alg"],"description":"\u98fd\u304d\u305f\u3089\u3084\u3081\u3088\u3046Galois\u7406\u8ad6(16)\u2015\u6709\u9650\u4f53\u518d\u8003 - \u3089\u3093\u3060\u3080\u306a\u8a18\u61b6\u3092\u8003\u5bdf\u3057\u3088\u3046\u3002 $p = 3,\\ n = 2$ \u306e\u5834\u5408\u3092\u8003\u3048\u308b\u3002 $\\mathbb{F}_3 = \\{0,1,2\\}$ \u305d\u3057\u3066\u305d\u306e\u4e0a\u306e\u65e2\u7d04\u591a\u9805\u5f0f\u3068\u3057\u3066\u3001 $X^2 + 1$ \u3092\u3068\u308b\u3002(\u98fd\u304d\u305f\u3089\u3084\u3081\u3088\u3046Galois\u7406\u8ad6(12)\u2015\u6709\u9650\u4f53\u3092\u8003\u3048\u308b - \u3089\u3093\u3060\u3080\u306a\u8a18\u61b6) \u3053\u306e\u591a\u9805\u5f0f\u306e\u6839\u306f $\\sqrt{2}, -\\sqrt{2}$ \u3067\u3042\u308b\u3002\u3069\u3061\u3089\u3067\u3082\u826f\u3044\u304c\u3001 $\\mathbb{F}_{3^2} = \\{a + b\\sqrt{2};\\ a,b \\in \\mathbb{F}_3 \\}$ \u3067\u3042\u308b\u3002\u5177\u4f53\u7684\u306b\u66f8\u304f\u3068\u3001 $\\mathbb{F}\u2026"}