{"id":549,"date":"2008-12-05T11:44:42","date_gmt":"2008-12-05T02:44:42","guid":{"rendered":"http:\/\/njet.oops.jp\/wordpress\/2008\/12\/05\/2%e6%ac%a1%e5%bd%a2%e5%bc%8f%e3%83%a1%e3%83%a21\/"},"modified":"2008-12-05T15:10:05","modified_gmt":"2008-12-05T06:10:05","slug":"2%e6%ac%a1%e5%bd%a2%e5%bc%8f%e3%83%a1%e3%83%a21","status":"publish","type":"post","link":"https:\/\/njet.oops.jp\/wordpress\/2008\/12\/05\/2%e6%ac%a1%e5%bd%a2%e5%bc%8f%e3%83%a1%e3%83%a21\/","title":{"rendered":"2\u6b21\u5f62\u5f0f\u30e1\u30e2(1)"},"content":{"rendered":"

[ \u5099\u5fd8\u9332 ]<\/p>\n


\n\u3059\u3063\u304b\u308a\u5fd8\u308c\u3066\u3044\u308b\u3001\u3068\u3044\u3046\u308f\u3051\u3067\u306f\u306a\u3044\u304c\u3001\u5fa9\u7fd2\u3082\u517c\u306d\u3066\u307e\u3063\u305f\u304f\u306e\u6700\u521d\u304b\u3089\u3084\u308a\u76f4\u3057\u4e2d\u3002<\/p>\n

\u6574\u6570\u4fc2\u6570\u306e2\u6b21\u5f62\u5f0f$f(x,y)=ax^2+bxy+cy^2$\u304c\u984c\u6750\u3002\u3053\u308c\u3092$(a,b,c)$\u3068\u7565\u8a18\u3059\u308b\u3002\u6700\u521d\u306e\u76ee\u6a19\u306f\u5e73\u65b9\u548c\u3067\u8868\u3055\u308c\u308b\u7d20\u6570$p=x^2+y^2$\u306a\u306e\u3067\u3001\u6b63\u5b9a\u5024(positive definite)\u306e\u5834\u5408\u306b\u9650\u5b9a\u3002\u5224\u5225\u5f0f$D=b^2-4ac$\u306f\u8ca0\u3068\u306a\u308b\u3002\u3053\u308c\u3089\u3092\u6574\u6570\u4fc2\u6570\u306e\uff11\u6b21\u5909\u63db
\n\u3000$x=pX+qY$, \u3000$y=rX+sY$ \u3000(\u305f\u3060\u3057 $ps-qr=1$)
\n\u3067\u5909\u63db\u3057\u3066\u884c\u304d\u3001\u4e92\u3044\u306b\u79fb\u308a\u5408\u3046\u3082\u306e\u3092\u300c\u6b63\u5f0f\u306b\u5bfe\u7b49(\u3042\u308b\u3044\u306f\u540c\u5024 properly equivalent)\u300d\u3068\u547c\u3093\u3067\u540c\u4e00\u8996\u3059\u308b\u3002\u5224\u5225\u5f0f$D$\u3092\u56fa\u5b9a\u3057\u305f\u3068\u304d\u3001\u540c\u4e00\u8996\u3055\u308c\u305f\u3082\u306e\u3092\u307e\u3068\u3081\u305f\u300c\u985e(class)\u300d\u306e\u500b\u6570\u306f\u6709\u9650\u3002\u3053\u308c\u3092\u985e\u6570(class number)\u3068\u3044\u3046\u3002<\/p>\n

\u5224\u5225\u5f0f$D$\u304c\u8ca0\u306e\u5834\u5408\u3001\u3064\u307e\u308a\u6b63\u5b9a\u5024\u306e\u5834\u5408\u306f\u3001\u985e\u306e\u4ee3\u8868\u3068\u3057\u3066
\n\\[ c\\geq a>0, \\qquad -a \\leq b \\leq a \\]
\n\u306a\u308b\u5f62\u5f0f\u304c\u9078\u3079\u308b\u3002\u3053\u308c\u3092\u300c\u7c21\u7d04\u5f62\u5f0f\u300d\u3068\u547c\u3076\u3002\u8a3c\u660e\u306f\u3044\u308d\u3044\u308d\u3042\u308b\u304c\u3001\u30ac\u30a6\u30b9\u306e\u8a3c\u660e\u304c\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u7684\u3067\u9762\u767d\u3044\u3002\u4e0e\u3048\u3089\u308c\u305f\u5f62\u5f0f\u306b\u300c\u53f3\u304b\u3089\u96a3\u63a5\u3059\u308b\u300d\u5f62\u5f0f\u3092\u6b21\u3005\u3068\u4f5c\u3063\u3066\u3044\u304f\u3002\u6709\u9650\u56de\u306e\u30b9\u30c6\u30c3\u30d7\u3067\u4e0a\u8a18\u306e\u7c21\u7d04\u5f62\u5f0f\u306b\u305f\u3069\u308a\u7740\u304f\u3053\u3068\u304c\u7c21\u5358\u306b\u793a\u3055\u308c\u308b\u3002<\/p>\n

\u7c21\u7d04\u5f62\u5f0f\u306f\u4e92\u3044\u306b\u5bfe\u7b49\u3067\u306a\u3044\u304b\u3068\u3044\u3046\u3068\u3001\u307b\u3068\u3093\u3069\u305d\u3046\u3060\u304c\u4f8b\u5916\u304c\u3042\u308b\u3002
\n\u3000$(a,a,c)$\u3068$(a,-a,c)$
\n\u3000$(a,b,a)$\u3068$(a,-b,a)$
\n\u306f\u4e92\u3044\u306b\u7b49\u5024\u3067\u3042\u308b\u3002\u3053\u306e\u4f8b\u5916\u3092\u9664\u3051\u3070\u3001\u7c21\u7d04\u5f62\u5f0f\u306f\u4e92\u3044\u306b\u5bfe\u7b49\u3067\u306f\u306a\u3044\u3002
\n<\/latex><\/p>\n","protected":false},"excerpt":{"rendered":"

[ \u5099\u5fd8\u9332 ] \u3059\u3063\u304b\u308a\u5fd8\u308c\u3066\u3044\u308b\u3001\u3068\u3044\u3046\u308f\u3051\u3067\u306f\u306a\u3044\u304c\u3001\u5fa9\u7fd2\u3082\u517c\u306d\u3066\u307e\u3063\u305f\u304f\u306e\u6700\u521d\u304b\u3089\u3084\u308a\u76f4\u3057\u4e2d\u3002 \u6574\u6570\u4fc2\u6570\u306e2\u6b21\u5f62\u5f0f$f(x,y)=ax^2+bxy+cy^2$\u304c\u984c\u6750\u3002\u3053\u308c\u3092$(a,b,c)$\u3068\u7565\u8a18\u3059\u308b\u3002\u6700\u521d\u306e\u76ee\u6a19\u306f […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[37,5],"tags":[],"class_list":["post-549","post","type-post","status-publish","format-standard","hentry","category-37","category-5"],"_links":{"self":[{"href":"https:\/\/njet.oops.jp\/wordpress\/wp-json\/wp\/v2\/posts\/549","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/njet.oops.jp\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/njet.oops.jp\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/njet.oops.jp\/wordpress\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/njet.oops.jp\/wordpress\/wp-json\/wp\/v2\/comments?post=549"}],"version-history":[{"count":0,"href":"https:\/\/njet.oops.jp\/wordpress\/wp-json\/wp\/v2\/posts\/549\/revisions"}],"wp:attachment":[{"href":"https:\/\/njet.oops.jp\/wordpress\/wp-json\/wp\/v2\/media?parent=549"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/njet.oops.jp\/wordpress\/wp-json\/wp\/v2\/categories?post=549"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/njet.oops.jp\/wordpress\/wp-json\/wp\/v2\/tags?post=549"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}