[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/13815#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/13815","headline":"Quadratklasse  – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2","name":"Quadratklasse  – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2","description":"before-content-x4 \u4ee3\u6570\u306b\u3042\u308a\u307e\u3059 \u6b63\u65b9\u5f62\u306e\u30af\u30e9\u30b9 \u305d\u306e\u7279\u5b9a\u306e\u540c\u7b49\u306e\u95a2\u4fc2\u306e\u7b49\u4fa1\u30af\u30e9\u30b9 \u6b63\u65b9\u5f62\u306e\u7b49\u4fa1 \u901a\u52e4\u30b0\u30eb\u30fc\u30d7\u3067\u3002\u3053\u308c\u3089\u306f\u3001\u3053\u306e\u30b0\u30eb\u30fc\u30d7\u306e\u6b63\u65b9\u5f62\u306e\u30b5\u30d6\u30b0\u30eb\u30fc\u30d7\u306e\u4e8c\u6b21\u30af\u30e9\u30b9\u3067\u3059\u3002\u3068\u308a\u308f\u3051\u3001\u6b63\u65b9\u5f62\u306e\u30af\u30e9\u30b9\u3068\u6b63\u65b9\u5f62\u306e\u7b49\u4fa1\u6027\u306e\u6982\u5ff5\u304c\u4f7f\u7528\u3055\u308c\u3066\u3044\u307e\u3059 after-content-x4 Quadrat\u30af\u30e9\u30b9\u306f\u3001\u3088\u308a\u4e00\u822c\u7684\u306b\u6587\u732e\u3067\u5b9a\u7fa9\u3055\u308c\u3066\u304a\u308a\u3001\u305d\u308c\u306b\u3088\u308a\u3001\u4e00\u822c\u7684\u306a\u30b0\u30eb\u30fc\u30d7\u7406\u8ad6\u7684\u7528\u8a9e\u306e\u7d50\u8ad6\u306f\u3001\u3088\u308a\u4e00\u822c\u7684\u306a\u6982\u5ff5\u306e\u672c\u8cea\u7684\u306a\u6838\u3068\u3057\u3066\u307b\u3068\u3093\u3069\u51fa\u73fe\u3057\u3066\u3044\u307e\u3059\u3002 \u300c\u6b63\u65b9\u5f62\u306e\u95a2\u4fc2\u300d\u306e\u4e00\u822c\u7684\u306a\u5b9a\u7fa9\u306f\u3001\u3053\u306e\u5b9a\u7fa9\u304c\u540c\u7b49\u306e\u95a2\u4fc2\u306b\u3064\u306a\u304c\u308b\u5834\u5408\u3001\u5e38\u306b\u8ce2\u660e\u306b\u4f7f\u7528\u3067\u304d\u308b\u3053\u3068\u3092\u4e3b\u5f35\u3057\u3066\u3044\u307e\u3059\u3002\u30b0\u30eb\u30fc\u30d7 – \u7406\u8ad6\u7684\u5b9a\u7fa9\u306f\u3001\u3044\u305a\u308c\u306b\u305b\u3088\u3001\u3044\u305a\u308c\u306e\u5834\u5408\u3067\u3082\u901a\u52e4\u30b0\u30eb\u30fc\u30d7\u306e\u540c\u7b49\u306e\u95a2\u4fc2\u3067\u3042\u308a\u3001\u6b63\u65b9\u5f62\u30af\u30e9\u30b9\u306f\u5b9f\u969b\u306b\u30b0\u30eb\u30fc\u30d7\u306e\u30b5\u30d6\u30b0\u30eb\u30fc\u30d7\u306e\u4e8c\u6b21\u30af\u30e9\u30b9\u3078\u306e\u5206\u5272\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002\u3053\u306e\u7279\u5225\u306a\u30b1\u30fc\u30b9\u3067\u306f\u3001ABEL\u30b0\u30eb\u30fc\u30d7\u306e\u30b5\u30d6\u30b0\u30eb\u30fc\u30d7\u306e\u901a\u5e38\u306e\u4ed5\u5207\u308a\u306e\u30bb\u30ab\u30f3\u30c0\u30ea\u30af\u30e9\u30b9\u306e\u3059\u3079\u3066\u306e\u6587\u3068\u30d7\u30ed\u30d1\u30c6\u30a3\u3092\u56db\u89d2\u3044\u30af\u30e9\u30b9\u306b\u9069\u7528\u3067\u304d\u307e\u3059\u3002 Table of Contents after-content-x4 \u4e00\u822c\u7684\u306a\u5b9a\u7fa9 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059","datePublished":"2021-12-10","dateModified":"2021-12-10","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/f82cade9898ced02fdd08712e5f0c0151758a0dd","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/f82cade9898ced02fdd08712e5f0c0151758a0dd","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/13815","wordCount":6395,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4\u4ee3\u6570\u306b\u3042\u308a\u307e\u3059 \u6b63\u65b9\u5f62\u306e\u30af\u30e9\u30b9 \u305d\u306e\u7279\u5b9a\u306e\u540c\u7b49\u306e\u95a2\u4fc2\u306e\u7b49\u4fa1\u30af\u30e9\u30b9 \u6b63\u65b9\u5f62\u306e\u7b49\u4fa1 \u901a\u52e4\u30b0\u30eb\u30fc\u30d7\u3067\u3002\u3053\u308c\u3089\u306f\u3001\u3053\u306e\u30b0\u30eb\u30fc\u30d7\u306e\u6b63\u65b9\u5f62\u306e\u30b5\u30d6\u30b0\u30eb\u30fc\u30d7\u306e\u4e8c\u6b21\u30af\u30e9\u30b9\u3067\u3059\u3002\u3068\u308a\u308f\u3051\u3001\u6b63\u65b9\u5f62\u306e\u30af\u30e9\u30b9\u3068\u6b63\u65b9\u5f62\u306e\u7b49\u4fa1\u6027\u306e\u6982\u5ff5\u304c\u4f7f\u7528\u3055\u308c\u3066\u3044\u307e\u3059        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4Quadrat\u30af\u30e9\u30b9\u306f\u3001\u3088\u308a\u4e00\u822c\u7684\u306b\u6587\u732e\u3067\u5b9a\u7fa9\u3055\u308c\u3066\u304a\u308a\u3001\u305d\u308c\u306b\u3088\u308a\u3001\u4e00\u822c\u7684\u306a\u30b0\u30eb\u30fc\u30d7\u7406\u8ad6\u7684\u7528\u8a9e\u306e\u7d50\u8ad6\u306f\u3001\u3088\u308a\u4e00\u822c\u7684\u306a\u6982\u5ff5\u306e\u672c\u8cea\u7684\u306a\u6838\u3068\u3057\u3066\u307b\u3068\u3093\u3069\u51fa\u73fe\u3057\u3066\u3044\u307e\u3059\u3002 \u300c\u6b63\u65b9\u5f62\u306e\u95a2\u4fc2\u300d\u306e\u4e00\u822c\u7684\u306a\u5b9a\u7fa9\u306f\u3001\u3053\u306e\u5b9a\u7fa9\u304c\u540c\u7b49\u306e\u95a2\u4fc2\u306b\u3064\u306a\u304c\u308b\u5834\u5408\u3001\u5e38\u306b\u8ce2\u660e\u306b\u4f7f\u7528\u3067\u304d\u308b\u3053\u3068\u3092\u4e3b\u5f35\u3057\u3066\u3044\u307e\u3059\u3002\u30b0\u30eb\u30fc\u30d7 – \u7406\u8ad6\u7684\u5b9a\u7fa9\u306f\u3001\u3044\u305a\u308c\u306b\u305b\u3088\u3001\u3044\u305a\u308c\u306e\u5834\u5408\u3067\u3082\u901a\u52e4\u30b0\u30eb\u30fc\u30d7\u306e\u540c\u7b49\u306e\u95a2\u4fc2\u3067\u3042\u308a\u3001\u6b63\u65b9\u5f62\u30af\u30e9\u30b9\u306f\u5b9f\u969b\u306b\u30b0\u30eb\u30fc\u30d7\u306e\u30b5\u30d6\u30b0\u30eb\u30fc\u30d7\u306e\u4e8c\u6b21\u30af\u30e9\u30b9\u3078\u306e\u5206\u5272\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002\u3053\u306e\u7279\u5225\u306a\u30b1\u30fc\u30b9\u3067\u306f\u3001ABEL\u30b0\u30eb\u30fc\u30d7\u306e\u30b5\u30d6\u30b0\u30eb\u30fc\u30d7\u306e\u901a\u5e38\u306e\u4ed5\u5207\u308a\u306e\u30bb\u30ab\u30f3\u30c0\u30ea\u30af\u30e9\u30b9\u306e\u3059\u3079\u3066\u306e\u6587\u3068\u30d7\u30ed\u30d1\u30c6\u30a3\u3092\u56db\u89d2\u3044\u30af\u30e9\u30b9\u306b\u9069\u7528\u3067\u304d\u307e\u3059\u3002 Table of Contents       (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u4e00\u822c\u7684\u306a\u5b9a\u7fa9 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u30b0\u30eb\u30fc\u30d7\u7406\u8ad6\u5b9a\u7fa9 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u4f53 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u6574\u5408\u6027\u30a8\u30ea\u30a2 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u4e00\u822c\u7684\u306a\u5b9a\u7fa9 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u591a\u5206 m {displaystyle m} \u30c0\u30d6\u30eb\u30c7\u30a3\u30ae\u30c3\u30c8\u30ea\u30f3\u30af\u304c\u305f\u304f\u3055\u3093\u3042\u308a\u307e\u3059 de {displaystyledot} \u3068 a {displaystyle a} \u3053\u306e\u30ea\u30f3\u30af\u306b\u95a2\u3057\u3066\u306f\u3001\u7a7a\u306e\u975e\u7a7a\u767d\u306e\u30b5\u30d6\u30bb\u30c3\u30c8\u304c\u7d42\u4e86\u3057\u307e\u3057\u305f\u3002\u305d\u306e\u5f8c\u3001\u4e57\u3063\u3066\u304f\u3060\u3055\u3044        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4m {displaystyle m} \u4e8c\u91cd\u8ddd\u96e2\u306e\u95a2\u4fc2 \u301c {displaystyle sim} \u5b9a\u7fa9\u306b\u3088\u3063\u3066\u5c0e\u5165\u3055\u308c\u307e\u3057\u305f m1\u301c m2{displaystyle m_ {1} sim m_ {2}} \u3001\u6edd\u306f\u8981\u7d20\u3067\u3059 a1\u3001 a2\u2208 a {displaystyle a_ {1}\u3001a_ {2} in} \u305d\u308c\u3092\u4e0e\u3048\u308b m1de a12= m2de a22{displaystyle m_ {1} cdot a_ {1}^{2} = m_ {2} cdot a_ {2}^{2}} \u306f\u3002 \u3053\u3053\u3067\u9069\u7528\u3055\u308c\u307e\u3059\uff1a \u305d\u306e\u5b9a\u7fa9\u306b\u3088\u308a\u3001\u95a2\u4fc2\u306f\u5e38\u306b\u53cd\u5c04\u7684\u3067\u5bfe\u79f0\u7684\u3067\u3059\u3002 \u30ea\u30f3\u30af\u304c\u95a2\u9023\u4ed8\u3051\u3089\u308c\u3066\u3044\u308b\u5834\u5408\u3001\u78ba\u304b\u306b\u63a8\u79fb\u7684\u3067\u3059 m {displaystyle m} \u305d\u3057\u3066\u901a\u52e4 a {displaystyle a} \u306f\u3002 \u4ee5\u4e0b\u3067\u306f\u3001\u3088\u308a\u5f31\u3044\u6761\u4ef6\u304c\u307b\u306b\u88dc\u9593\u306b\u5341\u5206\u3067\u3059\uff1a m\u2208M;a,b\u2208A{displaystyle min m ;; a\u3001bin a} \u5e38\u306b\u8981\u7d20\u304c\u5b58\u5728\u3057\u307e\u3059 c,d\u2208A{displaystyle c\u3001din a} \u3068\u306a\u308b\u3053\u3068\u306b\u3088\u3063\u3066 (m\u22c5a2)\u22c5b2=m\u22c5c2{displaystyle (mcdot a^{2})cdot b^{2}=mcdot c^{2}}\uff08\u95a2\u9023\u6027\u306e\u5f31\u4f53\u5316\uff09\u304a\u3088\u3073 a2\u22c5b2=d2{displaystyle a^{2}cdot b^{2}=d^{2};}\uff08\u6574\u6d41\u306e\u5f31\u4f53\u5316\uff09\u3002 \u95a2\u4fc2\u304c\u4ea4\u63db\u7684\u3067\u3042\u308b\u3001\u3059\u306a\u308f\u3061\u7b49\u4fa1\u95a2\u4fc2\u304c\u3042\u308b\u3059\u3079\u3066\u306e\u5834\u5408\u306b\u304a\u3044\u3066\u3001\u306e2\u3064\u306e\u8981\u7d20\u3068\u547c\u3070\u308c\u307e\u3059 m {displaystyle m} \u305d\u308c\u306f\u3001\u30b5\u30d6\u30bb\u30c3\u30c8\u306b\u95a2\u3057\u3066\uff08\u3055\u3089\u306b\u610f\u5473\u304c\u3042\u308b\uff09\u95a2\u4fc2\u3092\u6e80\u305f\u3057\u3066\u3044\u307e\u3059 a {displaystyle a} \u3002\u306e\u8981\u7d20\u3067\u3042\u308b\u3053\u306e\u95a2\u4fc2\u306e\u5404\u7b49\u4fa1\u30af\u30e9\u30b9 a {displaystyle a} \u542b\u3080\u3001\u5e73\u65b9\u30af\u30e9\u30b9\uff08\u3088\u308a\u72ed\u3044\u610f\u5473\u3067\uff09\u3092\u610f\u5473\u3057\u307e\u3059 m {displaystyle m} \u53c2\u7167\u3059\u308b\u3068 a {displaystyle a} \u3002 \u30b0\u30eb\u30fc\u30d7\u7406\u8ad6\u5b9a\u7fa9 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u591a\u5206 \uff08 g \u3001 de \uff09\uff09 {displaystyle\uff08g\u3001cdot\uff09} \u901a\u52e4\u30b0\u30eb\u30fc\u30d7\u3002\u6b21\u306b\u3001\u6b63\u65b9\u5f62\u306e\u5f62\u304c\u3042\u308a\u307e\u3059 Q \uff1a g \u2192 g ; g \u21a6 g2{displaystyle qcolon grightarrow g; gmapsto g^{2}} \u30b0\u30eb\u30fc\u30d7\u306e\u540c\u6027\u611b\u3002\u305d\u306e\u5199\u771f\u3001\u91cf g 2= { g 2‘ g \u2208 g } {displaystyle g^{2} = lbrace g^{2}\u30df\u30c3\u30c9\u30b8\u30f3\u30b0\u30ec\u30fc\u30b9} \u300c\u6b63\u65b9\u5f62\u300d\u306f\u306e\u30b5\u30d6\u30b0\u30eb\u30fc\u30d7\u3067\u3059 g {displaystyle g} \u305d\u3057\u3066\u3001\u3053\u306e\u30b5\u30d6\u30b0\u30eb\u30fc\u30d7\u306e\u4e8c\u6b21\u30af\u30e9\u30b9\u306f\u3001\u306e\u6b63\u65b9\u5f62\u30af\u30e9\u30b9\u3068\u547c\u3070\u308c\u307e\u3059 g {displaystyle g} \u3002 \u305d\u308c\u306f\u3001\u305d\u3053\u306b\u3042\u308b\u3068\u304d\u306e\u4e00\u822c\u7684\u306a\u5b9a\u7fa9\u306e\u7279\u5225\u306a\u30b1\u30fc\u30b9\u3067\u3059 m = a = g {displaystyle m = a = g} \u8a2d\u5b9a\u3055\u308c\u3066\u3044\u307e\u3059\u3002 \u6b63\u65b9\u5f62\u306e\u30a4\u30e9\u30b9\u30c8\u304c\u30b5\u30fc\u30d5\u306e\u5834\u5408\u3001\u30b0\u30eb\u30fc\u30d7\u5168\u4f53\u3092\u542b\u3080\u6b63\u65b9\u5f62\u306e\u30af\u30e9\u30b9\u306f1\u3064\u3060\u3051\u3067\u3059\u3002\u3053\u306e\u30b1\u30fc\u30b9\u306f\u3001\u30a4\u30e9\u30b9\u30c8\u304c\u7121\u8996\u3055\u308c\u305f\u3068\u304d\u306b\u6b63\u78ba\u306b\u6709\u9650\u30b0\u30eb\u30fc\u30d7\u3067\u767a\u751f\u3057\u3001\u3057\u305f\u304c\u3063\u3066\u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u306e\u6587\u306b\u5f93\u3063\u3066\u3001\u30b0\u30eb\u30fc\u30d7\u306e\u9806\u5e8f\u304c\u5947\u5999\u3067\u3042\u308b\u305f\u3081\u3001\u6b63\u78ba\u306b\u8a2d\u5b9a\u3055\u308c\u3001\u3057\u305f\u304c\u3063\u3066\u8981\u7d20\u306f\u307e\u3063\u3059\u3050\u306a\u9806\u5e8f\u3092\u6301\u3064\u3053\u3068\u306f\u3042\u308a\u307e\u305b\u3093\u3002 \u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306e\u6b63\u65b9\u5f62\u306e\u30af\u30e9\u30b9\u306e\u6570\u304c\u3088\u308a\u4e00\u822c\u7684\u3067\u3059 \uff08 g \uff1a g 2\uff09\uff09 {displaystyle\uff08g\uff1ag^{2}\uff09} \u6b63\u65b9\u5f62 g {displaystyle g} \u3002 \u4f53 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] 1\u3064\u306e\u4f53\u3067 \uff08 k \u3001 + \u3001 de \uff09\uff09 {displaystyle\uff08k\u3001+\u3001cdot\uff09} \u901a\u5e38\u3001\u4e57\u6cd5\u30b0\u30eb\u30fc\u30d7\u306b\u95a2\u3059\u308b\u6b63\u65b9\u5f62\u306e\u7b49\u4fa1\u6027\u3067\u3059 \uff08 k \u2217\u3001 de \uff09\uff09 {displaystyle\uff08k^{*}\u3001cdot\uff09} \u3044\u3064  \u4e8c\u6b21\u540c\u7b49\u6027\u3002 0\u306e\u7b49\u4fa1\u30af\u30e9\u30b9\uff08\u3055\u3089\u306a\u308b\u610f\u5473\u3067\uff09\u306fnull\u8981\u7d20\u306e\u307f\u3067\u69cb\u6210\u3055\u308c\u3001\u4ed6\u306e\u3059\u3079\u3066\u306f\u6b63\u65b9\u5f62\u306e\u30af\u30e9\u30b9\u3067\u3059 k {displaystyle k} \u4e00\u822c\u7684\u306a\u5b9a\u7fa9\u3068\u306e\u610f\u5473\u3067 \uff08 k \u2217\u3001 de \uff09\uff09 {displaystyle\uff08k^{*}\u3001cdot\uff09} \u3088\u308a\u72ed\u3044\u610f\u5473\u3067\u3001\u30b0\u30eb\u30fc\u30d7\u306e\u7406\u8ad6\u7684\u5b9a\u7fa9\u306e\u610f\u5473\u3067\u3002 \u6574\u5408\u6027\u30a8\u30ea\u30a2 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u6574\u5408\u6027\u9818\u57df\u3067 \uff08 r \u3001 + \u3001 de \uff09\uff09 {displaystyle\uff08r\u3001+\u3001cdot\uff09} \uff08\u30b7\u30f3\u30b0\u30eb\u30a8\u30ec\u30e1\u30f3\u30c8\u4ed8\u304d\uff09\u306f\u3001\u901a\u5e38 – \u4f53\u306e\u3088\u3046\u306b – \u77ed\u671f\u3001\u6574\u6d41\u30e2\u30ce\u30a4\u30c9\u306b\u95a2\u3059\u308b\u6b63\u65b9\u5f62\u306e\u7b49\u4fa1\u6027 \uff08 r \u2216 { 0 } \u3001 de \uff09\uff09 {displaystyle\uff08rsetminus lbrace 0rbrace\u3001cdot\uff09} \u3044\u3064  \u4e8c\u6b21\u540c\u7b49\u6027\u3002\u3053\u3053\u3067\u3082\u3001\u3059\u3079\u3066\u306e\u7b49\u4fa1\u30af\u30e9\u30b9\u306f\u9664\u3044\u3066\u3044\u307e\u3059 { 0 } {displaystyle lbrace 0rbrace} \u306e\u30b5\u30d6\u30bb\u30c3\u30c8 a = r \u2216 { 0 } {displaystyle a = rsetminus lbrace 0rbrace} \u3057\u305f\u304c\u3063\u3066\u3001\u306e\u6b63\u65b9\u5f62\u306e\u30af\u30e9\u30b9 r {displaystyle r} \uff08\u3088\u308a\u72ed\u3044\u610f\u5473\u3067\uff09\u3002 \u3055\u3089\u306b\u3001\u6574\u5408\u6027\u9818\u57df\u306e\u57cb\u3081\u8fbc\u307f\u3068\u306e\u6b63\u65b9\u5f62\u306e\u7b49\u4fa1\u6027\u306f\u3001\u305d\u306e\u5546\u306e\u4f53\u306b\u3042\u308a\u307e\u3059 quot \u2061 \uff08 r \uff09\uff09 {displaystyle operatorname {quot}\uff08r\uff09} \u4e92\u63db\u6027\uff1a\u6574\u5408\u6027\u9818\u57df\u306e2\u3064\u306e\u8981\u7d20\u306f\u3001\u30ea\u30f3\u30b0\u3067\u6b63\u65b9\u5f62\u306b\u76f8\u5f53\u3059\u308b\u3060\u3051\u3067\u3059\uff08\u3088\u308a\u6b63\u78ba\u306b\u306f\u3001\u57cb\u3081\u8fbc\u307f\u4e0b\u306e\u3053\u308c\u3089\u306e\u8981\u7d20\u306e\u753b\u50cf\uff09\u3082\u3001\u5546\u4f53\u3067\u306f\u6b63\u65b9\u5f62\u306b\u76f8\u5f53\u3057\u307e\u3059\uff08\u30b0\u30eb\u30fc\u30d7 – \u7406\u8ad6\u7684\u5b9a\u7fa9\u306e\u610f\u5473\u3067\u3082\uff09\u3002\u3055\u3089\u306b\u3001\u5546\u4f53\u306e\u5404\u6b63\u65b9\u5f62\u306e\u30af\u30e9\u30b9\u306b\u306f\u3001\u300c\u5168\u4f53\u306e\u300d\u8981\u7d20\u3001\u3064\u307e\u308a\u6574\u5408\u6027\u9818\u57df\u306e\u8981\u7d20\u306e\u57cb\u3081\u8fbc\u307f\u753b\u50cf\u304c\u542b\u307e\u308c\u3066\u3044\u307e\u3059\u3002 r {displaystyle r} \u3002 \u5b9f\u6570\u306e\u672c\u4f53\u306b\u306f\u3001\u6b63\u78ba\u306b2\u3064\u306e\u6b63\u65b9\u5f62\u306e\u30af\u30e9\u30b9\u3001\u3064\u307e\u308a\u6b63\u306e\u91cf\u3068\u8ca0\u306e\u5b9f\u6570\u306e\u4f53\u304c\u542b\u307e\u308c\u3066\u3044\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u4e00\u822c\u7684\u306b\u3059\u3079\u3066\u306e\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u30dc\u30c7\u30a3\u306b\u9069\u7528\u3055\u308c\u307e\u3059\u3002 \u8907\u96d1\u306a\u6570\u5b57\u306e\u672c\u4f53\u306b\u306f\u30011\u3064\u306e\u6b63\u65b9\u5f62\u306e\u30af\u30e9\u30b9\u306e\u307f\u304c\u542b\u307e\u308c\u3066\u3044\u307e\u3059\u3002 C\u2217= C\u2216 { 0 } {displaystyle mathbb {c} ^{*} = mathbb {c} setminus lbrace 0rbrace} \u3002\u3053\u308c\u306f\u3001\u3059\u3079\u3066\u306e\u4ee3\u6570\u4f53\u306b\u305d\u308c\u306b\u5fdc\u3058\u3066\u9069\u7528\u3055\u308c\u307e\u3059\u3002 \u5168\u4f53\u306e\u6574\u5408\u6027\u9818\u57df Z{displaystyle mathbb {z}} \u7121\u9650\u306e\u6570\u306e\u6b63\u65b9\u5f62\u30af\u30e9\u30b9\u304c\u542b\u307e\u308c\u3066\u3044\u307e\u3059\u3002 2\u3064\u306e\u6574\u6570\uff080\u3092\u9664\u304f\uff09\u306f\u3001\u88fd\u54c1\u304c\u6b63\u65b9\u5f62\u306e\u6570\u3001\u3064\u307e\u308a1\u306b\u76f8\u5f53\u3059\u308b\u65b9\u5411\u306b\u7b49\u4fa1\u3067\u3059\u3002\u6b63\u65b9\u5f62\u306e\u6570\u5b57\u306f\u3001\u4ee3\u8868\u30b7\u30b9\u30c6\u30e0\u3092\u5f62\u6210\u3057\u307e\u3059\u3002 \u6b8b\u308a\u306e\u30af\u30e9\u30b9\u30dc\u30c7\u30a3 k = Z\/p Z{displaystyle k = mathbb {z} \/pmathbb {z}} if\u306e\u5834\u5408\u306f1\u3064\u306e\u6b63\u65b9\u5f62\u306e\u30af\u30e9\u30b9\u306e\u307f\u304c\u542b\u307e\u308c\u3066\u3044\u307e\u3059 p = 2 {displaystyle p = 2} is\u3001\u305d\u3057\u3066\u6b63\u78ba\u306b2\u3064\u306e\u6b63\u65b9\u5f62\u306e\u30af\u30e9\u30b9\u306e\u5834\u5408 p {displaystyle p} \u5947\u6570\u306e\u30d7\u30e9\u30a4\u30e0\u3067\u3059\u3002\u6b21\u306e\u533a\u5225\u306f\u5e7e\u4f55\u5b66\u306b\u3068\u3063\u3066\u4f9d\u7136\u3068\u3057\u3066\u91cd\u8981\u3067\u3059\uff1a\u5947\u5999\u306a\u7d20\u6570\u3067\u3059 p {displaystyle p} \u30d5\u30a9\u30fc\u30e0\u304b\u3089 p = 4 de k + \u521d\u3081 \u3001 k \u2208 N{displaystyle p = 4cdot k+1\u3001; Kin Mathbb {n}}}} \u3001\u6b21\u306b\u3001-1\u30681\u5e73\u65b9\u306f\u540c\u7b49\u3067\u3059\u3002 p = 4 de k + 3 \u3001 k \u2208 N0{displaystyle p = 4cdot k+3\u3001; kin mathbb {n} _ {0}}} \u7570\u306a\u308b\u6b63\u65b9\u5f62\u306e\u30af\u30e9\u30b9\u306b\u6a2a\u305f\u308f\u3063\u3066\u3044\u307e\u3059\u3002 \uff08\u2192\u6b63\u65b9\u5f62\u306e\u4f11\u606f\u3001\u6b63\u65b9\u5f62\u306e\u76f8\u4e92\u95a2\u4fc2\u306e\u6cd5\u5247\u3001\u304a\u3088\u3073\u5e7e\u4f55\u5b66\u7684\u9069\u7528\u306b\u3064\u3044\u3066\u306f\u3001neulid\u524d\u306e\u30ec\u30d9\u30eb\u3092\u53c2\u7167\uff09\u3002 \u3059\u3079\u3066\u306e\u6709\u9650\u4f53 F2n{displaystyle mathbb {f} _ {2^{n}}} \u7279\u60272\u3067\u3001\u6b63\u78ba\u306b1\u3064\u306e\u6b63\u65b9\u5f62\u306e\u30af\u30e9\u30b9\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u3059\u3079\u3066\u306e\u7d14\u7c8b\u306a\u6b63\u65b9\u65b9\u7a0b\u5f0f\u306f\u3067\u3059 X2+ c = 0 {displaystyle x^{2}+c = 0} \u3053\u308c\u3089\u306e\u8eab\u4f53\u3067\u306f\u3001\u30d5\u30ed\u30d9\u30cb\u30e5\u65cf\u306e\u5f62\u3092\u6b63\u78ba\u306b\u4ecb\u3057\u3066 \u4e8c\u91cd\u30ab\u30a6\u30f3\u30c8 \u89e3\u6c7a\u3002 Quaternion Group\u306b\u306f\u3001\u975e\u914d\u4fe1\u306e\u4f8b\u304c\u767a\u751f\u3057\u307e\u3059 Q8= { \u00b1 \u521d\u3081 \u3001 \u00b1 \u79c1 \u3001 \u00b1 j \u3001 \u00b1 k } {displaystyle q_ {8} = lbrace pm 1\u3001pm i\u3001pm j\u3001pm krbrace} \u3002\u3053\u306e\u30b0\u30eb\u30fc\u30d7\u306f\u901a\u52e4\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u304c\u3001\u30bb\u30f3\u30bf\u30fc\u306e4\u3064\u306e\u4e8c\u6b21\u30af\u30e9\u30b9\u306f \u3068 \uff08 Q8\uff09\uff09 = \uff08 Q8)2= { \u00b1 \u521d\u3081 } {displaystyle z\uff08q_ {8}\uff09=\uff08q_ {8}\uff09^{2} = lbrace pm 1rbrace} \u30b0\u30eb\u30fc\u30d7\u306e\u6b63\u65b9\u5f62\u306e\u30af\u30e9\u30b9\uff08\u30b0\u30eb\u30fc\u30d7\u306b\u95a2\u3057\u3066 a = Q8{displaystyle a = q_ {8}} \u81ea\u5df1\uff09\u4e00\u822c\u7684\u306a\u5b9a\u7fa9\u306e\u610f\u5473\u3067\u3002\u3053\u306e\u30b0\u30eb\u30fc\u30d7\u306f\u6e96\u80fd\u306e\u591a\u91cd\u306a\u30b0\u30eb\u30fc\u30d7\u3067\u3082\u3042\u308b\u305f\u3081\uff08\u2192\u30c6\u30eb\u30ca\u30fc\u30d9\u30f3\u306b\u8a18\u8f09\u3055\u308c\u3066\u3044\u308b\u6e96\u8eab\u4f53\uff03\u6ce8\u65879\u306e\u4f8b J9{displaystyle j_ {9}} \uff09\u5408\u6210\u30b8\u30aa\u30e1\u30c8\u30ea\u306b\u8208\u5473\u304c\u3042\u308a\u307e\u3059\u3002\u6e96\u30dc\u30c7\u30a3\u306e\u305f\u3081\u306b J9{displaystyle j_ {9}} \u306f { 0 } \u222a \u3068 \uff08 Q8\uff09\uff09 {displaystyle lbrace 0rbrace\u30ab\u30c3\u30d7z\uff08q_ {8}\uff09} \u540c\u6642\u306b \u30ab\u30fc\u30f3 \u3002 Martin Aigner\u3001Dieter Jungnickel\uff08\u7de8\uff09\uff1a \u30b8\u30aa\u30e1\u30c8\u30ea\u3068\u30b0\u30eb\u30fc\u30d7\u3002 1981\u5e745\u6708\u3001\u30d9\u30eb\u30ea\u30f3\u5927\u5b66\u3067\u958b\u50ac\u3055\u308c\u305f\u30b3\u30ed\u30ad\u30a6\u30e0\u306e\u8b70\u4e8b\u9332 \u3002\u30b9\u30d7\u30ea\u30f3\u30ac\u30fc\u3001\u30d9\u30eb\u30ea\u30f3\/\u30cf\u30a4\u30c7\u30eb\u30d9\u30eb\u30af\/\u30cb\u30e5\u30fc\u30e8\u30fc\u30af1981\u3001ISBN 3-540-11166-2\u3002  \u30aa\u30ec\u30b0\u30fb\u30c8\u30e2\u30d3\u30c3\u30c1\u30fb\u30a4\u30dc\u30eb\u30c7\u30a3\u30f3\u3001\u30b8\u30e3\u30f3\u30fb\u30d4\u30a8\u30fc\u30eb\u30fb\u30c6\u30a3\u30ce\u30fc\u30eb\uff08\u7de8\uff09\uff1a \u4e8c\u6b21\u5f62\u5f0f\u306e\u4ee3\u6570\u7406\u8ad6\u306b\u304a\u3051\u308b\u5e7e\u4f55\u5b66\u7684\u65b9\u6cd5 \u3002\u30b5\u30de\u30fc\u30b9\u30af\u30fc\u30eb\u3001\u30ec\u30f3\u30ba\u30012000\u5e74\u3002\u30b9\u30d7\u30ea\u30f3\u30ac\u30fc\u3001\u30d9\u30eb\u30ea\u30f3\/\u30cf\u30a4\u30c7\u30eb\u30d9\u30eb\u30af\/\u30cb\u30e5\u30fc\u30e8\u30fc\u30af\/\u9999\u6e2f\/\u30ed\u30f3\u30c9\u30f3\/\u30df\u30e9\u30ce\/\u30d1\u30ea\/\u6771\u4eac2000\u3001ISBN 3-540-20728-7\uff08\u6570\u5b66\u306e\u8b1b\u7fa9\u30ce\u30fc\u30c8\u3001Vol\u30021835\uff09\u3002  Helmut Hasse\uff1a \u5408\u7406\u7684\u306a\u6570\u5b57\u306e\u672c\u4f53\u306e\u5e73\u65b9\u5f62\u72b6\u306b\u3088\u308b\u6570\u5b57\u306e\u8868\u73fe\u53ef\u80fd\u6027\u306b\u3064\u3044\u3066 \u3002\u306e\uff1a \u7d14\u7c8b\u304a\u3088\u3073\u5fdc\u7528\u6570\u5b66\u306e\u305f\u3081\u306e\u30b8\u30e3\u30fc\u30ca\u30eb \u3002 1923\u5e74\uff08 G\u00f6ttingenDigitizationCenter\u306e\u5168\u6587 \uff09\u3002  \u30cf\u30f3\u30d5\u30ea\u30fc\u30c9\u30ec\u30f3\u30c4\uff1a \u6b63\u65b9\u5f62\u306e\u5f62\u3068\u30b3\u30ea\u30cd\u30fc\u30c8\u30b0\u30eb\u30fc\u30d7 \u3002\u306e\uff1a \u6570\u5b66\u306e\u30a2\u30fc\u30ab\u30a4\u30d6 \u3002 \u30d0\u30f3\u30c9  18 \u3002\u30cf\u30ce\u30fc\u30d0\u30fc1962\u3001 S.  110\u2013119 \u3001doi\uff1a 10.1007\/BF01650054 \u3002  Armin Leutbecher\uff1a \u756a\u53f7\u7406\u8ad6\uff1a\u4ee3\u6570\u306e\u7d39\u4ecb \u3002\u30b9\u30d7\u30ea\u30f3\u30ac\u30fc\u3001\u30d9\u30eb\u30ea\u30f3\/\u30cf\u30a4\u30c7\u30eb\u30d9\u30eb\u30af\/\u30cb\u30e5\u30fc\u30e8\u30fc\u30af1996\u3001ISBN 3-540-58791-8\u3002        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/13815#breadcrumbitem","name":"Quadratklasse  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