{"type":"rich","url":"https://randommemory.hatenablog.com/entry/2016/09/24/183621","published":"2016-09-24 18:36:21","author_name":"derwind","author_url":"https://blog.hatena.ne.jp/derwind/","image_url":null,"blog_title":"\u3089\u3093\u3060\u3080\u306a\u8a18\u61b6","description":"\u4f8b1 \u6a19\u65700\u306e\u4f53\u6216\u306f\u3001\u6a19\u6570\u304c2\u3067\u306f\u306a\u3044\u6709\u9650\u4f53\u306e\u4ee3\u6570\u62e1\u5927\u4f53\u3092\u8003\u3048\u308b\u3002 $[L:K] = 2$ \u3068\u3059\u308b\u3002Galois\u7406\u8ad6(46)\u2015\u6b63\u898f\u62e1\u5927\u88dc\u8db3(2)\u3068\u5c11\u3057\u6574\u7406 - \u3089\u3093\u3060\u3080\u306a\u8a18\u61b6\u3067\u898b\u305f\u3088\u3046\u306b\u30012\u6b21\u62e1\u5927\u306e\u5834\u5408\u306b\u306f\u6b63\u898f\u62e1\u5927\u3068\u306a\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3088\u3046\u3002 \u3053\u306e\u6642\u3001\u3042\u308b $\\alpha \\in L\\backslash K$ \u304c\u3068\u308c\u3066\u3001\u305d\u306e\u6700\u5c0f\u591a\u9805\u5f0f $P_\\min(\\alpha,K)$ \u306e\u6b21\u6570\u306f2\u3068\u306a\u308b\u3002 $P_\\min(\\alpha,K) = X^2 + aX + b$ \u3068\u8003\u3048\u308b\u3068\u3001\u305d\u306e\u5224\u5225\u5f0f $\\Delta = a^2 - 4b$ \u3092\u8003\u3048\u308b\u3068\u3001 $L = K(\\sqrt{\\Delta})$ \u306b\u306a\u3063\u3066\u3044\u308b\u3002 \u2026","html":"<iframe src=\"https://hatenablog-parts.com/embed?url=https%3A%2F%2Frandommemory.hatenablog.com%2Fentry%2F2016%2F09%2F24%2F183621\" title=\"Galois\u7406\u8ad6(49)\u2015\u30ac\u30ed\u30a2\u7fa4\u306e\u8a08\u7b97\u4f8b - \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>","height":"190","version":"1.0","blog_url":"https://randommemory.hatenablog.com/","categories":["math-alg"],"title":"Galois\u7406\u8ad6(49)\u2015\u30ac\u30ed\u30a2\u7fa4\u306e\u8a08\u7b97\u4f8b","provider_name":"Hatena Blog","provider_url":"https://hatena.blog","width":"100%"}