[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/jp\/wiki6\/archives\/10502#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/jp\/wiki6\/archives\/10502","headline":"\u5fae\u5206\u74b0 – Wikipedia","name":"\u5fae\u5206\u74b0 – Wikipedia","description":"\u3053\u306e\u8a18\u4e8b\u306f\u691c\u8a3c\u53ef\u80fd\u306a\u53c2\u8003\u6587\u732e\u3084\u51fa\u5178\u304c\u5168\u304f\u793a\u3055\u308c\u3066\u3044\u306a\u3044\u304b\u3001\u4e0d\u5341\u5206\u3067\u3059\u3002\u51fa\u5178\u3092\u8ffd\u52a0\u3057\u3066\u8a18\u4e8b\u306e\u4fe1\u983c\u6027\u5411\u4e0a\u306b\u3054\u5354\u529b\u304f\u3060\u3055\u3044\u3002\u51fa\u5178\u691c\u7d22?:\u00a0“\u5fae\u5206\u74b0”\u00a0\u2013\u00a0\u30cb\u30e5\u30fc\u30b9\u00a0\u00b7 \u66f8\u7c4d\u00a0\u00b7 \u30b9\u30ab\u30e9\u30fc\u00a0\u00b7 CiNii\u00a0\u00b7 J-STAGE\u00a0\u00b7 NDL\u00a0\u00b7 dlib.jp\u00a0\u00b7 \u30b8\u30e3\u30d1\u30f3\u30b5\u30fc\u30c1\u00a0\u00b7 TWL\uff082015\u5e7410\u6708\uff09 \u6570\u5b66\u306b\u304a\u3044\u3066\u3001\u5fae\u5206\u74b0\uff08\u3073\u3076\u3093\u304b\u3093\u3001\u82f1: differential ring\uff09\u3001\u5fae\u5206\u4f53\uff08\u3073\u3076\u3093\u305f\u3044\u3001\u82f1: differential field\uff09\u3001\u5fae\u5206\u591a\u5143\u74b0\uff08\u3073\u3076\u3093\u305f\u3052\u3093\u304b\u3093\u3001\u82f1: differntial algebra\uff09\u306f\u3001\u305d\u308c\u305e\u308c\u6709\u9650\u500b\u306e\u5fae\u5206\uff08\u82f1\u8a9e\u7248\uff09\uff08\u52a0\u6cd5\u7684\u307e\u305f\u306f\u7dda\u578b\u306a\u5358\u9805\u6f14\u7b97\u3067\u7a4d\u306e\u5fae\u5206\u6cd5\u5247\uff08\u30e9\u30a4\u30d7\u30cb\u30c3\u30c4\u5247\uff09\u3092\u6e80\u8db3\u3059\u308b\uff09\u3092\u5099\u3048\u305f\u74b0\u3001\u4f53\u3001\u591a\u5143\u74b0\u3067\u3042\u308b\u3002\u5fae\u5206\u74b0\u306e\u5fae\u5206\u306f\u3057\u3070\u3057\u3070 \u2202, \u03b4, d, D","datePublished":"2020-12-24","dateModified":"2022-09-14","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/jp\/wiki6\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/jp\/wiki6\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?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:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/6\/64\/Question_book-4.svg\/50px-Question_book-4.svg.png","url":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/6\/64\/Question_book-4.svg\/50px-Question_book-4.svg.png","height":"39","width":"50"},"url":"https:\/\/wiki.edu.vn\/jp\/wiki6\/archives\/10502","about":["Wiki"],"wordCount":5539,"articleBody":"\u3053\u306e\u8a18\u4e8b\u306f\u691c\u8a3c\u53ef\u80fd\u306a\u53c2\u8003\u6587\u732e\u3084\u51fa\u5178\u304c\u5168\u304f\u793a\u3055\u308c\u3066\u3044\u306a\u3044\u304b\u3001\u4e0d\u5341\u5206\u3067\u3059\u3002\u51fa\u5178\u3092\u8ffd\u52a0\u3057\u3066\u8a18\u4e8b\u306e\u4fe1\u983c\u6027\u5411\u4e0a\u306b\u3054\u5354\u529b\u304f\u3060\u3055\u3044\u3002\u51fa\u5178\u691c\u7d22?:\u00a0“\u5fae\u5206\u74b0”\u00a0\u2013\u00a0\u30cb\u30e5\u30fc\u30b9\u00a0\u00b7 \u66f8\u7c4d\u00a0\u00b7 \u30b9\u30ab\u30e9\u30fc\u00a0\u00b7 CiNii\u00a0\u00b7 J-STAGE\u00a0\u00b7 NDL\u00a0\u00b7 dlib.jp\u00a0\u00b7 \u30b8\u30e3\u30d1\u30f3\u30b5\u30fc\u30c1\u00a0\u00b7 TWL\uff082015\u5e7410\u6708\uff09\u6570\u5b66\u306b\u304a\u3044\u3066\u3001\u5fae\u5206\u74b0\uff08\u3073\u3076\u3093\u304b\u3093\u3001\u82f1: differential ring\uff09\u3001\u5fae\u5206\u4f53\uff08\u3073\u3076\u3093\u305f\u3044\u3001\u82f1: differential field\uff09\u3001\u5fae\u5206\u591a\u5143\u74b0\uff08\u3073\u3076\u3093\u305f\u3052\u3093\u304b\u3093\u3001\u82f1: differntial algebra\uff09\u306f\u3001\u305d\u308c\u305e\u308c\u6709\u9650\u500b\u306e\u5fae\u5206\uff08\u82f1\u8a9e\u7248\uff09\uff08\u52a0\u6cd5\u7684\u307e\u305f\u306f\u7dda\u578b\u306a\u5358\u9805\u6f14\u7b97\u3067\u7a4d\u306e\u5fae\u5206\u6cd5\u5247\uff08\u30e9\u30a4\u30d7\u30cb\u30c3\u30c4\u5247\uff09\u3092\u6e80\u8db3\u3059\u308b\uff09\u3092\u5099\u3048\u305f\u74b0\u3001\u4f53\u3001\u591a\u5143\u74b0\u3067\u3042\u308b\u3002\u5fae\u5206\u74b0\u306e\u5fae\u5206\u306f\u3057\u3070\u3057\u3070 \u2202, \u03b4, d, D \u7b49\u306e\u8a18\u53f7\u3092\u7528\u3044\u3066\u8868\u3055\u308c\u308b\u3002\u5fae\u5206\u4f53\u306e\u81ea\u7136\u306a\u4f8b\u3068\u3057\u3066\u3001\u8907\u7d20\u6570\u4f53\u4e0a\u306e\u4e00\u5909\u6570\u6709\u7406\u95a2\u6570\u4f53 C(t) \u306b\u5fae\u5206\u3068\u3057\u3066\u666e\u901a\u306e\u610f\u5473\u3067\u306e\u5fae\u5206 D = d\u2044dt \u3092\u3068\u3063\u305f\u3082\u306e\u3092\u6319\u3052\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002  \u305d\u306e\u3088\u3046\u306a\u4ee3\u6570\u7cfb\u81ea\u8eab\u306e\u7814\u7a76\u304a\u3088\u3073\u305d\u308c\u3089\u4ee3\u6570\u7cfb\u306e\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u4ee3\u6570\u7684\u7814\u7a76\u306b\u5bfe\u3059\u308b\u5fdc\u7528\u3092\u7814\u7a76\u3059\u308b\u5206\u91ce\u3092\u5fae\u5206\u4ee3\u6570\u5b66 (Differntial Algebra) \u3068\u547c\u3076\u3002\u5fae\u5206\u74b0\u306f\u30b8\u30e7\u30bb\u30d5\u30fb\u30ea\u30c3\u30c8\uff08\u82f1\u8a9e\u7248\uff09\u304c\u5c0e\u5165\u3057\u305f[1]\u3002\u74b0 R \u3068\u305d\u306e\u4e0a\u306e\u5199\u50cf \u2202: R \u2192 R \u306e\u7d44 (R, \u2202) \u304c\u5fae\u5206\u74b0\u3067\u3042\u308b\u3068\u306f\u3001\u4e8c\u3064\u306e\u6761\u4ef6 \u2202(x+y)=\u2202x+\u2202y\u2202(xy)=(\u2202x)y+x(\u2202y)(\u2200x,y\u2208R){displaystyle {begin{aligned}&partial (x+y)=partial x+partial y&partial (xy)=(partial x)y+x(partial y)end{aligned}}quad (forall x,yin R)} \u3092\u6e80\u305f\u3059\u3001\u3059\u306a\u308f\u3061 \u2202 \u304c R \u306e\u52a0\u6cd5\u7fa4\u306e\u9593\u306e\u6e96\u540c\u578b\uff08\u52a0\u6cd5\u7684\u5199\u50cf\uff09\u3067\u7a4d\u306b\u95a2\u3057\u3066\u30e9\u30a4\u30d7\u30cb\u30c3\u30c4\u5247\u3092\u6e80\u8db3\u3059\u308b\u3082\u306e\u3067\u3042\u308b\u3068\u304d\u306b\u8a00\u3046\u3002\u6ce8\u610f\u3059\u3079\u304d\u306f\u3001\u3053\u3053\u3067\u74b0\u306f\u975e\u53ef\u63db\u3068\u306a\u308b\u5834\u5408\u3082\u3042\u308a\u3046\u308b\u304b\u3089\u3001\u901a\u5e38\u3088\u304f\u7528\u3044\u3089\u308c\u308b\u5fae\u5206\u3092\u5f8c\u308d\u306b\u66f8\u304f\u3042\u308b\u7a2e\u306e\u6a19\u6e96\u5f62 \u2202(xy) = x\u22c5\u2202y + y\u22c5\u2202x \u306f\u7a4d\u306e\u53ef\u63db\u6027\u304c\u4fdd\u8a3c\u3055\u308c\u306a\u3044\u5834\u9762\u3067\u306f\u9069\u5207\u3067\u306a\u3044\u3053\u3068\u3067\u3042\u308b\u3002  \u4f5c\u7528\u7d20\u306e\u30ec\u30d9\u30eb\u3067\u898b\u308c\u3070\u3001\u74b0\u306e\u4e57\u6cd5\u3092 M: R \u00d7 R \u3068\u3057\u3066 \u2202\u2218M=M\u2218(\u2202\u00d7id)+M\u2218(id\u00d7\u2202){displaystyle partial circ M=Mcirc (partial times operatorname {id} )+Mcirc (operatorname {id} times partial )} \u306a\u308b\u7b49\u5f0f\u3068\u3057\u3066\u7a4d\u306e\u6cd5\u5247\u3092\u66f8\u304f\u3053\u3068\u3082\u3067\u304d\u308b\u3002\u305f\u3060\u3057\u3001f \u00d7 g \u306f\u5199\u50cf\u306e\u76f4\u7a4d\u3067\u3001\u5404\u5bfe (x, y) \u3092\u5bfe (f(x), g(x) \u3078\u5199\u3059\u3002\u5fae\u5206\u4f53\u306f\u3001\u5fae\u5206\u3092\u5099\u3048\u308b\u53ef\u63db\u4f53 K \u3092\u8a00\u3046\u3002\u3053\u3053\u3067\u3001\u5fae\u5206\u306f\u4f53\u306e\u69cb\u9020\u3068\u4e21\u7acb\u3059\u308b\uff08\u3064\u307e\u308a\u9664\u6cd5\u3068\u6574\u5408\u3059\u308b\uff09\u3088\u3046\u306a\u3082\u306e\u3092\u3068\u308b\u3079\u304d\u3067\u3042\u308b\u304c\u3001\u3088\u304f\u77e5\u3089\u308c\u305f\u5546\u306e\u5fae\u5206\u6cd5\u5247 \u2202(uv)=\u2202(u)v\u2212u\u2202(v)v2{displaystyle partial left({frac {u}{v}}right)={frac {partial (u)v-upartial (v)}{v^{2}}}} \u306f\u7a4d\u306e\u6cd5\u5247\u304b\u3089\u5c0e\u304b\u308c\u308b\u3002\u5b9f\u969b\u306b   \u2202(uv\u00d7v)=\u2202(u){textstyle partial ({tfrac {u}{v}}times v)=partial (u)} \u304c\u6210\u308a\u7acb\u3064\u3079\u304d\u3068\u3053\u308d\u3001\u5de6\u8fba\u306b\u7a4d\u306e\u6cd5\u5247\u3092\u9069\u7528\u3057\u3066 \u2202(uv)v+uv\u2202(v)=\u2202(u){textstyle partial ({frac {u}{v}})v+{frac {u}{v}}partial (v)=partial (u)} \u3068\u306a\u308b\u304b\u3089\u3001\u2202(u\/v ) \u3067\u6574\u7406\u3059\u308c\u3070\u6240\u671f\u306e\u5f0f\u3092\u5f97\u308b\u3002\u5fae\u5206\u4f53 K \u306b\u5bfe\u3057\u3066\u305d\u306e\u5b9a\u6570\u4f53 (field of constants) \u306f k := {u \u2208 K | \u2202(u) = 0} \u3067\u4e0e\u3048\u3089\u308c\u308b\u3002Table of Contents\u5fae\u5206\u591a\u5143\u74b0[\u7de8\u96c6]\u64ec\u5fae\u5206\u4f5c\u7528\u7d20\u306e\u74b0[\u7de8\u96c6]\u95a2\u9023\u9805\u76ee[\u7de8\u96c6]\u53c2\u8003\u6587\u732e[\u7de8\u96c6]\u95a2\u9023\u6587\u732e[\u7de8\u96c6]\u5916\u90e8\u30ea\u30f3\u30af[\u7de8\u96c6]\u5fae\u5206\u591a\u5143\u74b0[\u7de8\u96c6]\u4f53 K \u4e0a\u306e\u5fae\u5206\u591a\u5143\u74b0\u306f\u3001\u30b9\u30ab\u30e9\u30fc\u4e57\u6cd5\u3068\u4e21\u7acb\u3059\u308b\u5fae\u5206\u3092\u5099\u3048\u305f K-\u591a\u5143\u74b0 A \u3092\u8a00\u3046\u3002\u3059\u306a\u308f\u3061\u3001\u5404\u5fae\u5206 \u2202 \u306f\u4fc2\u6570\u4f53\u3068\u5143\u3054\u3068\u306b\u53ef\u63db: k\u2208K\u27f9\u2202(kx)=k\u2202x(\u2200x\u2208A){displaystyle kin Kimplies partial (kx)=kpartial xquad (forall xin A)} \u3067\u3042\u308b\u3002\u3053\u308c\u306f\u4f5c\u7528\u7d20\u306e\u30ec\u30d9\u30eb\u3067\u306f\u3001\u30b9\u30ab\u30e9\u30fc\u4e57\u6cd5\u3092\u5b9a\u7fa9\u3059\u308b\u74b0\u6e96\u540c\u578b \u03b7: K \u2192 A \u3092\u7528\u3044\u3066 \u2202\u2218M\u2218(\u03b7\u00d7id)=M\u2218(\u03b7\u00d7\u2202){textstyle partial circ Mcirc (eta times operatorname {id} )=Mcirc (eta times partial )} \u3068\u66f8\u3051\u308b\u30ea\u30fc\u74b0\u4e0a\u306e\u5fae\u5206\u4f53 K \u4e0a\u306e\u30ea\u30fc\u74b0 g{displaystyle {mathfrak {g}}} \u4e0a\u306e\u5fae\u5206 \u2202 \u3068\u306f\u3001K-\u7dda\u578b\u5199\u50cf \u2202:g\u2192g{textstyle partial colon {mathfrak {g}}to {mathfrak {g}}} \u3067\u3042\u3063\u3066\u3001\u30ea\u30fc\u62ec\u5f27\u7a4d\u306b\u95a2\u3059\u308b\u30e9\u30a4\u30d7\u30cb\u30c3\u30c4\u5247 \u2202([a,b])=[a,\u2202(b)]+[\u2202(a),b]{displaystyle partial ([a,b])=[a,partial (b)]+[partial (a),b]} \u3092\u6e80\u305f\u3059\u3082\u306e\u3092\u3044\u3046\u306e\u3067\u3042\u3063\u305f\u3002\u4efb\u610f\u306e a\u2208g{displaystyle ain {mathfrak {g}}} \u306b\u5bfe\u3057 ad(a): x \u21a6 [a, x]\uff08\u3064\u307e\u308a ad \u306f\u30ea\u30fc\u74b0\u306e\u968f\u4f34\u8868\u73fe\uff09\u304c g{displaystyle {mathfrak {g}}} \u4e0a\u306e\u5fae\u5206\u3068\u306a\u308b\u3053\u3068\u306f\u30e4\u30b3\u30d3\u306e\u7b49\u5f0f\u306b\u3088\u308b\u3002\u3053\u306e\u3088\u3046\u306b\u5f97\u3089\u308c\u308b\u5fae\u5206\u3092\u3001\u30ea\u30fc\u74b0 g{displaystyle {mathfrak {g}}} \u306e\u5185\u90e8\u5fae\u5206\u3068\u547c\u3076\u3002\u30ea\u30fc\u74b0\u306e\u5185\u90e8\u5fae\u5206\u3092\u3001\u305d\u306e\u666e\u904d\u5305\u7d61\u74b0\u3078\u5ef6\u9577\u3057\u3066\u3001\u666e\u904d\u5305\u7d61\u74b0\u3092\u5fae\u5206\u591a\u5143\u74b0\u3068\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002A \u304c\u5358\u4f4d\u7684\u591a\u5143\u74b0\u306a\u3089\u3070\u3001\u305d\u306e\u4e57\u6cd5\u5358\u4f4d\u5143\u3092 1 \u3068\u3057\u3066 \u2202(1) = 0 \u3067\u3042\u308b\uff08\u2202(1) = \u2202(1 \u00d7 1) = \u2202(1) + \u2202(1)\uff09\u3002\u5f93\u3063\u3066\u3001\u4f8b\u3048\u3070 \u6a19\u6570 0 \u306e\u5fae\u5206\u4f53 K \u306f\u3001\u5e38\u306b\u6709\u7406\u6570\u4f53\u3092 K \u306e\u5b9a\u6570\u4f53\u306e\u90e8\u5206\u4f53\u3068\u3057\u3066\u542b\u3080\u3002\u4efb\u610f\u306e\u74b0\u306f\u3001\u96f6\u6e96\u540c\u578b\uff08\u305d\u306e\u4efb\u610f\u306e\u5143\u3092\u96f6\u5143\u306b\u5199\u3059\uff09\u3092\u81ea\u660e\u306a\u5fae\u5206\u3068\u307f\u3066\u3001\u5fae\u5206\u74b0\u3067\u3042\u308b\u3002\u4e00\u5909\u6570\u6709\u7406\u4fc2\u6570\u6709\u7406\u5f0f\u4f53 Q(t) \u306f\u3001\u2202(t) = 1 \u3068\u6b63\u898f\u5316\u3059\u308b\u3053\u3068\u3067\u6c7a\u307e\u308b\u3001\u5fae\u5206\u4f53\u3068\u3057\u3066\u4e00\u610f\u306a\u69cb\u9020\u3092\u6301\u3064\uff08\u4f53\u306e\u516c\u7406\u304a\u3088\u3073\u5fae\u5206\u306e\u516c\u7406\u306f\u3001\u5fae\u5206\u304c t \u306b\u95a2\u3059\u308b\u901a\u5e38\u306e\u5fae\u5206\u3068\u306a\u308b\u3053\u3068\u3092\u4fdd\u8a3c\u3059\u308b\uff09\u3002\u4f8b\u3048\u3070\u3001\u7a4d\u306e\u53ef\u63db\u6027\u3068\u7a4d\u306e\u5fae\u5206\u516c\u5f0f\u306b\u3088\u308a\u3001\u2202(u2) = u\u22c5\u2202(u) + \u2202(u)\u22c5u= 2u\u2202(u) \u304c\u6210\u308a\u7acb\u3064\u3002\u5fae\u5206\u4f53 Q(t) \u306f\u5fae\u5206\u65b9\u7a0b\u5f0f \u2202(u) = u \u306e\u89e3\u3092\u6301\u305f\u306a\u3044\u304c\u3001\u6307\u6570\u95a2\u6570 et \u3092\u542b\u3080\u3088\u308a\u5927\u304d\u3044\u5fae\u5206\u4f53\u306b\u62e1\u5927\u3057\u3066\u3001\u3053\u306e\u5fae\u5206\u65b9\u7a0b\u5f0f\u304c\u305d\u3053\u3067\u89e3\u3092\u6301\u3064\u3088\u3046\u306b\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u4efb\u610f\u306e\u5fae\u5206\u65b9\u7a0b\u5f0f\u7cfb\u306b\u5bfe\u3059\u308b\u89e3\u3092\u6709\u3059\u308b\u5fae\u5206\u4f53\u3092\u5fae\u5206\u7684\u9589\u4f53\uff08\u82f1\u8a9e\u7248\uff09\u3068\u3044\u3046\u3002\u81ea\u7136\u306a\u4ee3\u6570\u7684\u3082\u3057\u304f\u306f\u5e7e\u4f55\u5b66\u7684\u5bfe\u8c61\u3068\u3057\u3066\u306f\u73fe\u308c\u306a\u3044\u304c\u3001\u3053\u306e\u3088\u3046\u306a\u5fae\u5206\u4f53\u306f\u5b58\u5728\u3059\u308b\u3002\uff08\u6fc3\u5ea6\u3092\u9069\u5f53\u306b\u4e0a\u304b\u3089\u6291\u3048\u308b\u3068\u304d\uff09\u3059\u3079\u3066\u306e\u5fae\u5206\u4f53\u306f\u3001\u5358\u4e00\u306e\u5927\u304d\u306a\u5fae\u5206\u7684\u9589\u4f53\u306e\u4e2d\u306b\u57cb\u3081\u8fbc\u3081\u308b\u3002\u5fae\u5206\u4f53\u306f\u3001\u5fae\u5206\u30ac\u30ed\u30a2\u7406\u8ad6\u306e\u7814\u7a76\u5bfe\u8c61\u3067\u3042\u308b\u3002\u64ec\u5fae\u5206\u4f5c\u7528\u7d20\u306e\u74b0[\u7de8\u96c6]\u5fae\u5206\u74b0\u304a\u3088\u3073\u5fae\u5206\u591a\u5143\u74b0 R \u306f\u3001\u3057\u3070\u3057\u3070\u305d\u308c\u3089\u306e\u4e0a\u306e\u64ec\u5fae\u5206\u4f5c\u7528\u7d20\u306e\u74b0 R((\u03be\u22121))={\u2211nn:rn\u2208R}{displaystyle R((xi ^{-1}))={biggl {}sum _{nn)=\u2211k=0mr(\u2202ks)(mk)\u03bem+n\u2212k{displaystyle (rxi ^{m})(sxi ^{n})=sum _{k=0}^{m}r(partial ^{k}s){m choose k}xi ^{m+n-k}} \u3067\u5b9a\u7fa9\u3055\u308c\u308b\u3002(mk){textstyle {m choose k}} \u306f\u4e8c\u9805\u4fc2\u6570\u3067\u3042\u308b\u3002\u3053\u3053\u3067\u3001\u6052\u7b49\u5f0f \u03be\u22121r=\u2211n=0\u221e(\u22121)n(\u2202nr)\u03be\u22121\u2212n{displaystyle xi ^{-1}r=sum _{n=0}^{infty }(-1)^{n}(partial ^{n}r)xi ^{-1-n}} \u306b\u306f\u6052\u7b49\u5f0f (\u22121n)=(\u22121)n{textstyle {-1 choose n}=(-1)^{n}} \u304a\u3088\u3073 r\u03be\u22121=\u2211n=0\u221e\u03be\u22121\u2212n(\u2202nr){textstyle rxi ^{-1}=sum _{n=0}^{infty }xi ^{-1-n}(partial ^{n}r)} \u304c\u7528\u3044\u3089\u308c\u3066\u3044\u308b\u3053\u3068\u306b\u6ce8\u610f\u3002\u95a2\u9023\u9805\u76ee[\u7de8\u96c6]\u53c2\u8003\u6587\u732e[\u7de8\u96c6]\u95a2\u9023\u6587\u732e[\u7de8\u96c6]Buium, Alexandru (1994), Differential Algebra and Diophantine Geometry, Actualit\u00e9s math\u00e9matiques, Hermann\u00a0.Kaplansky, Irving (1957), An Introduction to Differential Algebra, Actualit\u00e9s scientifiques et industrielles, Hermann, https:\/\/books.google.com\/books?id=R4TQAAAAMAAJ\u00a0.Kolchin, E. R. (1973). Differential Algebra and Algebraic Groups. Pure and applied mathematics. 54. New York: Academic Press. http:\/\/www4.ncsu.edu\/~singer\/foraachen\/DAAG.pdf\u00a0Marker, David (1996). \u201c2: Model theory of differential fields\u201d. In Marker, D.; Messmer, M; Pillay, A.. Model theory of fields. Lecture notes in Logic. 5. Berlin: Springer Verlag. pp.\u00a038\u2013113. https:\/\/projecteuclid.org\/euclid.lnl\/1235423156\u00a0Magid, Andy R. (1994), Lectures on Differential Galois Theory, University Lecture Series, 7, American Mathematical Society, ISBN\u00a09780821882665, https:\/\/books.google.com\/books?id=cJ9vByhPqQ8C\u00a0 (review (PDF) )\u5916\u90e8\u30ea\u30f3\u30af[\u7de8\u96c6]"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki6\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki6\/archives\/10502#breadcrumbitem","name":"\u5fae\u5206\u74b0 – Wikipedia"}}]}]