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\u767a\u751f\u3059\u308b\u6570\u5024\u306e\u30b9\u30e9\u30a4\u30c9\u304b\u3089Do-it-yourself\u306e\u62e1\u5927\u3068\u306f\u7570\u306a\u308a\u3001\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u30fc\u4ee3\u6570\u306f\u5e38\u306b\u6b63\u78ba\u306b\u8a08\u7b97\u3059\u308b\u3068\u3044\u3046\u4e3b\u5f35\u3092\u6301\u3063\u3066\u3044\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u57fa\u790e\u3068\u306a\u308b\u69cb\u9020\uff08\u901a\u5e38\u306f\u30b0\u30eb\u30fc\u30d7\u3001\u30ea\u30f3\u30b0\u3001\u307e\u305f\u306f\u30dc\u30c7\u30a3\uff09\u306e\u8981\u4ef6\u3092\u6307\u5b9a\u3059\u308b\u3053\u3068\u304c\u57fa\u672c\u7684\u306b\u5fc5\u8981\u3067\u3059\u3002 Table of Contents \u30b0\u30eb\u30fc\u30d7 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] 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\u3059\u3079\u3066\u306e\u6709\u9650\u30b0\u30eb\u30fc\u30d7\u3092\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u30fc\u306b\u8868\u793a\u3067\u304d\u307e\u3059\u3002\u305f\u3068\u3048\u3070\u3001\u591a\u74b0\u7fa4\u306e\u5834\u5408\u3001\u7279\u5b9a\u306e\u6761\u4ef6\u4e0b\u3067\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u304c\u3042\u308a\u307e\u3059\u3002        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u4e88\u6e2c\u53ef\u80fd\u306a\u30ea\u30f3\u30b0 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u30ea\u30f3\u30b0\u304c\u547c\u3070\u308c\u307e\u3059 \u4e88\u6e2c\u53ef\u80fd\u306a \uff08\u307e\u305f\u306f\u300c\u52b9\u679c\u7684\u300d\uff09\u6b21\u306e\u6761\u4ef6\u304c\u9069\u7528\u3055\u308c\u308b\u5834\u5408\uff1a 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\u5b8c\u5168\u306a\u6570\u5b57\u3092\u4f7f\u7528\u3057\u305f\u6b63\u78ba\u306a\u7b97\u8853\u306e\u30bf\u30b9\u30af\u3068\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u6642\u9593\u306e\u8907\u96d1\u3055\u3092\u5206\u985e\u3059\u308b\u5834\u5408\u306f\u3001\u6700\u521d\u306b\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u30fc\u30e2\u30c7\u30eb\u3092\u4f7f\u7528\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3055\u307e\u3056\u307e\u306a\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u30fc\u30e2\u30c7\u30eb\u306e\u8b70\u8ad6\u306f\u3001\u3053\u306e\u7ae0\u306e\u8907\u96d1\u3055\u306b\u8a18\u8f09\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u6bd4\u8f03\u7684\u30ad\u30e3\u30c3\u30c1\u30fc\u306a\u30e2\u30c7\u30eb\u306f\u3001\u30af\u30e9\u30b7\u30c3\u30af\u306a\u30c1\u30e5\u30fc\u30ea\u30f3\u30b0\u30de\u30b7\u30f3\u306e\u30d0\u30ea\u30a2\u30f3\u30c8\u3067\u3042\u308b\u30de\u30eb\u30c1\u30d0\u30f3\u30c9\u306e\u305d\u3073\u3048\u7acb\u3064\u6a5f\u68b0\u3067\u3001\u305d\u308c\u305e\u308c\u57f7\u7b46\/\u8aad\u307f\u53d6\u308a\u30d8\u30c3\u30c9\u3092\u5099\u3048\u305f\u3044\u304f\u3064\u304b\u306e\u976d\u5e2f\u304c\u3042\u308a\u307e\u3059\u3002\u5fc5\u8981\u306b\u5fdc\u3058\u3066\u3001Landau\u8868\u8a18\u3068\u306e\u8907\u96d1\u3055\u306e\u63a8\u5b9a\u306b\u3064\u3044\u3066\u306f\u3001\u6307\u5b9a\u306e\u4e0b\u3067 \u30ed\u30b0 {displaystyle operatorname {log}} \u975e\u6307\u5b9a\u30d9\u30fc\u30b9\u3067\u306e\u5bfe\u6570 1&#8243;>\u4f7f\u7528\u6e08\u307f\u3002\u5fc5\u8981\u306a\u30d3\u30c3\u30c8\u64cd\u4f5c\u306e\u6570\u306f\u3001Landau\u8868\u8a18\u306e\u5165\u529b\u306e\u30d3\u30c3\u30c8\u9577\u306b\u4f9d\u5b58\u3059\u308b\u6642\u9593\u306e\u5c3a\u5ea6\u3068\u3057\u3066\u9078\u629e\u3055\u308c\u307e\u3059\u3002 \u5b8c\u5168\u306a\u6570\u5b57\u3092\u6301\u3064\u6b63\u78ba\u306a\u7b97\u8853\u306e\uff08\u30d3\u30c3\u30c8\uff09\u8907\u96d1\u3055\u306e\u6b63\u78ba\u306a\u6570\u5b66\u7684\u9069\u5fdc\u306f\u3001\u6700\u521d\u306b\u7dcf\u6570\u306e\u30d3\u30c3\u30c8\u9577\u306e\u6b63\u78ba\u306a\u6c7a\u5b9a\u304b\u3089\u958b\u59cb\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002 a \u2208 \u3068 {displaystyle ain mathbb {z}} \u30bc\u30ed\u3067\u306f\u306a\u3044\u306e\u3067\u3001\u305d\u3046\u3067\u3059 l \uff08 a \uff09\uff09 \uff1a= \u230a \u30ed\u30b0 2\u2061 | a | \u230b {displaystyle l\uff08a\uff09\uff1a= lfloor log _ {2} | a | rfloor} \u8a2d\u5b9a;\u3055\u3089\u306b\u3001 l \uff08 0 \uff09\uff09 \uff1a= \u521d\u3081 {displaystyle l\uff080\uff09\uff1a= 1} \u5b9a\u7fa9\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u5168\u4f53\u306e\u6570\u306e\u7279\u5b9a\u306e\u30b9\u30c8\u30ec\u30fc\u30b8\u306b\u306f\u3001\u30b5\u30a4\u30f3\u306b\u306f\u5c11\u306a\u304f\u3068\u30821\u3064\u306e\u30d3\u30c3\u30c8\u304c\u5fc5\u8981\u3067\u3059\u3002 \u6a19\u8b58\u306e\u5146\u5019\u306e\u30bf\u30b9\u30af SGN \u2061 \uff08 a \uff09\uff09 \u3001 {displaystyle operatorname {sgn}\uff08a\uff09\u3001} \u30cd\u30ac\u306e\u8a08\u7b97  &#8211;  a {displaystyle -a} \u91d1\u984d\u3068\u540c\u69d8\u306b | a | {displaystyle | a |} \u3059\u3079\u3066\u7dda\u5f62\u6642\u9593\u3067\u3059 o \uff08 l \uff09\uff09 {displaystyle o\uff08l\uff09} \u3068 l = l \uff08 a \uff09\uff09 {displaystyle l = l\uff08a\uff09} \u5b9f\u884c\u53ef\u80fd;\u8ffd\u52a0 a + b {displaystyle a+b} 2\u3064\u306e\u6570\u5b57\u306e\u6bd4\u8f03\u3082\u540c\u69d8\u3067\u3059 a < b {displaystyle a \u7dda\u5f62\u6642\u9593\u3067\u3059 o \uff08 l \uff09\uff09 {displaystyle o\uff08l\uff09} \u3068 l = m a \u30d0\u30c4 \uff08 l \uff08 a \uff09\uff09 \u3001 l \uff08 b \uff09\uff09 \uff09\uff09 {displaystyle l = {rm {max}}\uff08l\uff08a\uff09\u3001l\uff08b\uff09\uff09} \u4f55\u304b\u3092\u7ba1\u7406\u3059\u308b\u3002 n -\u30b7\u30d5\u30c8 2 n de a {displaystyle 2^{n} cdot a} \u5165\u3063\u3066\u3044\u307e\u3059 o \uff08 n + l \uff09\uff09 {displaystyle o\uff08n+l\uff09} \u5b9f\u884c\u53ef\u80fd\u3002 \u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u30fc\u4ee3\u6570\u306e\u81ea\u660e\u3067\u306f\u306a\u3044\u7d50\u679c\u306f\u3001\u5897\u6b96\u3059\u308b\u3068\u3044\u3046\u8a8d\u8b58\u3067\u3059 a de b {displaystyle acdot b} \u3067\u3088\u308a\u306f\u308b\u304b\u306b\u901f\u3044 o \uff08 l 2\uff09\uff09 {displaystyle oleft\uff08l^{2}\u53f3\uff09} \uff08\u3053\u308c\u306f\u3001\u30ca\u30a4\u30fc\u30d6\u4e57\u7b97\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306b\u5bfe\u5fdc\u3057\u3066\u3044\u307e\u3059\uff09\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u30ab\u30e9\u30ba\u30d0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u5099\u3048\u305f\u30a2\u30ca\u30c8\u30ea\u30ab\u30e9\u30ba\u30d0\u306f\u3001\u6700\u521d\u306f\u52a0\u901f\u3092\u9054\u6210\u3057\u307e\u3057\u305f\u3002\u3053\u308c\u306f\u3001Toom Cook\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3068\u3044\u3046\u7528\u8a9e\u306b\u5305\u307e\u308c\u3066\u3044\u308b\u3001\u3055\u3089\u306b\u4e00\u822c\u7684\u306a\u30a2\u30eb\u30b4\u30ea\u30b7\u30c3\u30af\u30d5\u30a1\u30df\u30ea\u30fc\u306e\u7279\u5225\u306a\u30b1\u30fc\u30b9\u3068\u3057\u3066\u8a8d\u8b58\u3055\u308c\u307e\u3057\u305f\u3002\u753b\u671f\u7684\u306a\u306e\u306f\u305d\u306e\u5f8c\u30011971\u5e74\u306b1971\u5e74\u306b\u30a2\u30fc\u30ce\u30eb\u30c9\u30fb\u30b7\u30a7\u30fc\u30f3\u30cf\u30fc\u30b8\u3068\u30f4\u30a9\u30eb\u30ab\u30fc\u30fb\u30b9\u30c8\u30e9\u30b9\u306b\u57fa\u3065\u3044\u3066\u3044\u305f\u30b7\u30a7\u30fc\u30f3\u30cf\u30fc\u30b8\u30fb\u30b9\u30c8\u30e9\u30c3\u30bb\u30f3\u30fb\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u3057\u305f\u3002 o \uff08 l de \u30ed\u30b0 l de \u30ed\u30b0 \u30ed\u30b0 l \uff09\uff09 {displaystyle o\uff08lcdot log\u3001lcdot log\u3001log\u3001l\uff09} \u898b\u305b\u3073\u3089\u304b\u3059\u3002 \u300c\u7d20\u6734\u306a\u300d\u4e57\u7b97\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u304c\u3069\u308c\u307b\u3069\u8907\u96d1\u3067\u3042\u308b\u304b\u3092\u8003\u3048\u308b\u3068\u3001\u3053\u306e\u8907\u96d1\u3055\u306f\u975e\u5e38\u306b\u300c\u9ad8\u901f\u300d\u306b\u898b\u3048\u307e\u3059\u3002\u305f\u3060\u3057\u3001\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u975e\u5e38\u306b\u8907\u96d1\u3067\u30d7\u30ed\u30b0\u30e9\u30e0\u304c\u96e3\u3057\u3044\u305f\u3081\u3001\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u30fc\u30a2\u30eb\u30d0\u30e0\u30b7\u30b9\u30c6\u30e0\u306b\u306f\u307e\u3060\u52b9\u7387\u7684\u306a\u5b9f\u88c5\u306f\u3042\u308a\u307e\u305b\u3093\u3002 \u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u30fc\u4ee3\u6570\u5168\u4f53\u3067\u306e\u6574\u6570\u4e57\u7b97\u306e\u8907\u96d1\u3055\u306f\u7d76\u5bfe\u306b\u91cd\u8981\u3067\u3042\u308b\u305f\u3081\u3001\u3053\u308c\u306b\u3064\u3044\u3066\u306f\u77ed\u3044\u8868\u8a18\u6cd5\u304c\u884c\u308f\u308c\u307e\u3057\u305f \u03c6 \uff08 l \uff09\uff09 \uff1a= o \uff08 l de \u30ed\u30b0 l de \u30ed\u30b0 \u30ed\u30b0 l \uff09\uff09 {displaystyle psi\uff08l\uff09\uff1a= o\uff08lcdot log\u3001lcdot log\u3001log\u3001l\uff09} \u7d39\u4ecb\u3055\u308c\u305f\u3002\u3053\u306e\u300c\u9ad8\u901f\u300d\u306a\u6574\u6570\u306e\u4e57\u7b97\u3092\u88c5\u5099\u3057\u3066\u3044\u308b\u305f\u3081\u3001\u7b97\u8853\u306e\u305f\u3081\u306e\u57fa\u672c\u7684\u306a\u7b97\u8853\u306e\u30ab\u30bf\u30ed\u30b0 \u3068 {displaystyle mathbb {z}} \u6b21\u306e\u3088\u3046\u306b\u5b8c\u4e86\u3059\u308b\uff1a\u8a08\u7b97\u306e\u30bf\u30b9\u30af a n {displaystyle a^{n}} \u5165\u3063\u3066\u3044\u307e\u3059 o \uff08 \u03c6 \uff08 n l \uff09\uff09 \uff09\uff09 {displaystyle oleft\uff08psi\uff08nl\uff09\u53f3\uff09} \u5b9f\u884c\u53ef\u80fd;\u4e8c\u9805\u4fc2\u6570\u306e\uff08\u540c\u6642\uff09\u8a08\u7b97\u7528 (n0)\u22ef (nn){displaystyle {n choose 0} cdots {n choose n}} \u306a\u308a\u307e\u3059 o \uff08 n de \u03c6 \uff08 n \uff09\uff09 \uff09\uff09 {displaystyle oleft\uff08ncdot psi\uff08n\uff09\u53f3\uff09} \u5fc5\u8981\u3067\u3059\u3002\u6574\u6570\u90e8\u9580 a \/ b {displaystyle a\/b} \uff08\u7d50\u679c\u3068\u3057\u3066\u5546\u3068\u4f11\u606f\uff09\u304c\u5fc5\u8981\u3067\u3059 o \uff08 llm\u22c5\u03c8(lm)\uff09\uff09 {displaystyle oleft\uff08{frac {l} {l_ {m}}} cdot psi\uff08l_ {m}\uff09}} \u3002 \u6700\u5927\u306e\u5171\u901a\u5206\u5272\u306e\u8a08\u7b97 g c d \uff08 a \u3001 b \uff09\uff09 {displaystyle {rm {gcd}}\uff08a\u3001b\uff09} \u5fc5\u8981\u3067\u3059 o \uff08 (llm+loglm)\u22c5\u03c8(lm)\uff09\uff09 {displaystyle oleft\uff08\u5de6\uff08{frac {l} {l_ {m}}}+{rm {log}}\u3001l_ {m}\u53f3\uff09cdot psi\uff08l_ {m}\uff09\u53f3\uff09}} \u3002 \u540c\u3058\u8907\u96d1\u3055\u3082\u3042\u308a\u307e\u3059 g c d \u305d\u3046\u3067\u3059 \u30d0\u30c4 \uff08 a \u3001 b \uff09\uff09 {displaystyle {rm {gcdex}}\uff08a\u3001b\uff09} \u305d\u308c\u306b\u5fdc\u3058\u3066\u3001d\u3002 H. kofactors \u306e \u3001 \u306e {displaystyle u\u3001v} \u3068 g c d \uff08 a \u3001 b \uff09\uff09 = \u306e a + \u306e b {displaystyle {rm {gcd}}\uff08a\u3001b\uff09= ua+vb} \u8a08\u7b97\u3055\u308c\u307e\u3059\u3002 \u5408\u7406\u7684\u306a\u6570\u5b57\u3092\u6301\u3064\u52b9\u7387\u7684\u306a\u6b63\u78ba\u306a\u7b97\u8853 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u6b63\u78ba\u306a\u7b97\u8853\u306e\u524d Q {displaystyle mathbb {q}} \u5177\u4f53\u7684\u306b\u5b9f\u884c\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u5408\u7406\u7684\u306a\u6570\u5b57\u306e\u6a19\u6e96\u8868\u73fe\uff08\u8868\u73fe\uff09\u3092\u6700\u521d\u306b\u898b\u3064\u3051\u306a\u3051\u308c\u3070\u306a\u308a\u307e\u305b\u3093\u3002\u3053\u306e\u554f\u984c\u306f\u3001\u6574\u6570\u306e\u6b63\u78ba\u306a\u7b97\u8853\u306b\u306f\u73fe\u308c\u307e\u305b\u3093\u3067\u3057\u305f\u3002\u5408\u7406\u7684\u306a\u6570\u5024\u306f\u3001\u5168\u4f53\u306e\u6570\u304b\u3089\u306e\u300c\u610f\u5473\u306e\u3042\u308b\u300d\u9aa8\u6298\u306e\u540c\u7b49\u306e\u30af\u30e9\u30b9\u3067\u3059\u3002\u305f\u3068\u3048\u3070\u3001\u3067\u3059 \u521d\u3081 2 {displaystyle {frac {1} {2}}} \u3068 2 4 {displaystyle {frac {2} {4}}} \u540c\u3058\u5408\u7406\u7684\u306a\u6570\u306e\u7570\u306a\u308b\u4ee3\u8868\u8005\u3002 \u6709\u7406\u6570\u306e\u6700\u3082\u4e00\u822c\u7684\u306a\u6a19\u6e96\u8868\u73fe\u306f\u3001\u30e1\u30fc\u30bf\u30fc\u3068\u5206\u6bcd\u304b\u3089\u3059\u3079\u3066\u306e\u4e00\u822c\u7684\u306a\u9664\u6570\u3092\u6e1b\u3089\u3059\u3053\u3068\u306b\u3088\u3063\u3066\u6c7a\u5b9a\u3055\u308c\u307e\u3059\u3002\u3059\u3079\u3066\u306e\u5408\u7406\u7684\u306a\u6570\u306f\u3001\u660e\u3089\u304b\u306b\u9aa8\u6298\u306e\u77ed\u7e2e\u306b\u3088\u308b\u3082\u306e\u3067\u3059\u3002 pq{displaystyle {frac {p} {q}}} \u3068 p \u2208 \u3068 \u3001 {displaystyle pin mathbb {z}\u3001}  Q \u2208 n {displaystyle qin mathbb {n}} \u3068 ggT\uff08 p \u3001 Q \uff09\uff09 = \u521d\u3081 {displaystyle {rm {ggt}}\uff08p\u3001q\uff09= 1} \u8868\u73fe\u53ef\u80fd\u3002\u3053\u306e\u5b9a\u7fa9\u304c\u884c\u308f\u308c\u305f\u3089\u3001\u3059\u3079\u3066\u306e\u521d\u7b49\u64cd\u4f5c\u306b\u306f Q {displaystyle mathbb {q}} \u6dfb\u52a0\u3084\u4e57\u7b97\u306a\u3069\u3001\u7d50\u679c\u306e\u9aa8\u6298\u306e\u30e1\u30fc\u30bf\u30fc\u3068\u5206\u6bcd\u304b\u3089\u6700\u5927\u306e\u5171\u901a\u5206\u5272\u8005\u304b\u3089\u8131\u843d\u3059\u308b\u30bf\u30b9\u30af\u3002 \u6b63\u78ba\u306a\u7b97\u8853\u306e\u7d50\u679c\u306b\u611f\u8b1d\u3057\u307e\u3059 \u3068 {displaystyle mathbb {z}} \u64cd\u4f5c\u3067\u3059 a + b \u3001 a  &#8211;  b \u3001 a de b \u3001 a \/ b {displaystyle a+b\u3001quad a-b\u3001quad acdot b\u3001quad a\/b} \u3059\u3079\u3066\u8907\u96d1\u3067\u3059 o \uff08 \u03c8(l)\u22c5logl\uff09\uff09 {displaystyle oleft\uff08psi\uff08l\uff09cdot {rm {log}}\u3001lright\uff09} \u5b9f\u884c\u53ef\u80fd\u3002\u7dda\u5f62\u306e\u8907\u96d1\u3055\u3067\u76f4\u7dda\u7684\u306a\u8907\u96d1\u3055\u3067\u5408\u7406\u7684\u306a\u6570\u5b57\u3092\u8ffd\u52a0\u3067\u304d\u308b\u3068\u3044\u3046\u5e0c\u671b\u306b\u5225\u308c\u3092\u544a\u3052\u306a\u3051\u308c\u3070\u306a\u308a\u307e\u305b\u3093\u3002 \u5e78\u3044\u306a\u3053\u3068\u306b\u3001\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u52a9\u3051\u3092\u501f\u308a\u3066\u3001\u6700\u5927\u306e\u5171\u901a\u5206\u5272\u306e\u8a08\u7b97\u3092\u975e\u5e38\u306b\u52b9\u7387\u7684\u306b\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u3001\u5909\u5316\u3059\u308b\u30d0\u30ea\u30a2\u30f3\u30c8\u306b\u304a\u3044\u3066\u3001\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u30fc\u4ee3\u6570\u306e\u591a\u304f\u306e\u5834\u6240\u3067\u4e3b\u5c0e\u7684\u306a\u5f79\u5272\u3092\u679c\u305f\u3057\u307e\u3059\u3002 \u211a[x]\u306e\u591a\u9805\u5f0f\u3092\u4f7f\u7528\u3057\u305f\u52b9\u7387\u7684\u306a\u6b63\u78ba\u306a\u7b97\u8853 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u7b97\u8853\u3092\u884c\u3046\u3060\u3051\u3067\u5341\u5206\u3067\u3059 \u3068 [ \u30d0\u30c4 ] {displaystyle mathbb {z} left [xright]} \u64cd\u4f5c\u304c\u3068\u8003\u3048\u308b\u4f5c\u6226\u304b\u3089\u4f5c\u6226\u3078\u306e\u305d\u308c\u305e\u308c\u306e\u9664\u5916\u3092\u901a\u3058\u3066\u3001\u7dca\u5bc6\u306b\u5408\u7406\u7684\u306a\u30dd\u30ea\u30ce\u30fc\u30e0\u6574\u6570\u591a\u9805\u5f0f\u3067\u8ffd\u8de1\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u30dd\u30ea\u30ce\u30fc\u30e0\u306e\u5834\u5408 f \u2208 \u3068 [ \u30d0\u30c4 ] {displaystyle fin mathbb {z} [x]} \uff08\u4fc2\u6570\uff09\u9577\u3055\u3092\u5b9a\u7fa9\u3057\u307e\u3059 l \uff08 f \uff09\uff09 {displaystyle l\uff08f\uff09} \u500b\u3005\u306e\u4fc2\u6570\u306e\u9577\u3055\u306e\u6700\u5927\u5024\u3068\u3057\u3066\u3002 \u6b21\u306e\u30e9\u30f3\u30bf\u30a4\u30e0\u30c6\u30fc\u30d6\u30eb\u306b\u3064\u3044\u3066\u3001\u91cd\u8981\u306a\u8a08\u7b97\u306e\u554f\u984c \u3068 [ \u30d0\u30c4 ] {displaystyle mathbb {z} [x]} \u4ee5\u4e0b\u3092\u51e6\u65b9\u3057\u307e\u3057\u3087\u3046\u3002 f \u3001 g \u2208 \u3068 [ \u30d0\u30c4 ] {displaystyle f\u3001gin mathbb {z} left [xright]} \u5b66\u4f4d\u304b\u3089 d f= \u81ea\u5206\u81ea\u8eab \u2061 f {displaystyle d_ {f} = deg f} \u307e\u305f\u3002 d g= \u81ea\u5206\u81ea\u8eab \u2061 g \u3001 {displaystyle d_ {g} = deg g\u3001} \u3055\u3089\u306b\u9060\u304f d = \u30de\u30c3\u30af\u30b9 \uff08 d f\u3001 d g\uff09\uff09 \u3001 d m= \u5206 \uff08 d f\u3001 d g\uff09\uff09 {displaystyle d = max\uff08d_ {f}\u3001d_ {g}\uff09\u3001d_ {m} = min\uff08d_ {f}\u3001d_ {g}\uff09} \u3001 \u9577\u3055 l f= l \uff08 f \uff09\uff09 {displaystyle l_ {f} = l\uff08f\uff09} \u307e\u305f\u3002 l g= l \uff08 g \uff09\uff09 \u3001 {displaystyle l_ {g} = l\uff08g\uff09\u3001} \u3055\u3089\u306b\u9060\u304f l = \u30de\u30c3\u30af\u30b9 \uff08 l f\u3001 l g\uff09\uff09 {displaystyle l = max\uff08l_ {f}\u3001l_ {g}\uff09} \u3068 l m= \u5206 \uff08 l f\u3001 l g\uff09\uff09 {displaystyle l_ {m} = min\uff08l_ {f}\u3001l_ {g}\uff09} \u3001 \u305d\u306e\u96a3\u3067\u3059 a \u2208 \u3068 {displaystyle ain mathbb {z}} \u30d3\u30c3\u30c8\u9577 l a= l \uff08 a \uff09\uff09 {displaystyle l_ {a} = l\uff08a\uff09} \u3002 \u6b21\u306b\u3001\uff08\u30d3\u30c3\u30c8\u306e\u8907\u96d1\u3055\u306b\u3088\u308b\u3068\uff09\u6700\u901f\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u6b21\u306e\u30e9\u30f3\u30bf\u30a4\u30e0\u30c6\u30fc\u30d6\u30eb\u306b\u5c0e\u304d\u307e\u3059\u3002 \u30c9\u30a4\u30c4\u8a9e &#8211; \u8a00\u8a9e\u6587\u5b66\uff1a \u82f1\u8a9e &#8211; \u8a00\u8a9e\u6587\u5b66\uff1a PeterB\u00fcrgisser\u3001Michael Clausen\u3001Mohammad Amin Shrollahi\uff1a \u4ee3\u6570\u7684\u8907\u96d1\u3055\u7406\u8ad6 \uff08= \u500b\u3005\u306e\u8868\u73fe\u306b\u304a\u3051\u308b\u6570\u5b66\u79d1\u5b66\u306e\u57fa\u672c\u7684\u306a\u6559\u3048\u3002 315\uff09\u3002\u30b9\u30d7\u30ea\u30f3\u30ac\u30fc\u3001\u30d9\u30eb\u30ea\u30f3u\u3002 a\u3002 1997\u3001ISBN 3-540-60582-7\uff08 \u30ec\u30d3\u30e5\u30fc \uff09\u3002 Arjeh M. Cohen\u3001Hans Cuypers\u3001Hans Sterk\uff1a \u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u30fc\u4ee3\u6570\u306e\u30bf\u30d1\u30b9 \uff08= \u6570\u5b66\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3068\u8a08\u7b97\u3002 4\uff09\u3002\u30b9\u30d7\u30ea\u30f3\u30ac\u30fc\u3001\u30d9\u30eb\u30ea\u30f3u\u3002 a\u3002 1999\u3001ISBN 3-540-63480-0\u3002 \u30c7\u30d3\u30c3\u30c9\u30fb\u30b3\u30c3\u30af\u30b9\u3001\u30b8\u30e7\u30f3\u30fb\u30ea\u30c8\u30eb\u3001\u30c9\u30ca\u30eb\u30fb\u30aa\u30b7\u30a7\u30a2\uff1a \u7406\u60f3\u3001\u54c1\u7a2e\u3001\u304a\u3088\u3073\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3002 \u7b2c2\u7248\u200b\u200b\u3002\u30b9\u30d7\u30ea\u30f3\u30ac\u30fc\u3001\u30cb\u30e5\u30fc\u30e8\u30fc\u30afNY UA\u3002 A. 1997\u3001ISBN 0-387-94680-2 Joachim von Zur Gathen\u3001J\u00fcrgenGerhard\uff1a \u73fe\u4ee3\u306e\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u30fc\u4ee3\u6570\u3002 \u7b2c2\u7248\u200b\u200b\u3002\u30b1\u30f3\u30d6\u30ea\u30c3\u30b8\u5927\u5b66\u51fa\u7248\u5c40\u3001\u30b1\u30f3\u30d6\u30ea\u30c3\u30b8u\u3002 a\u3002 2003\u3001ISBN 0-521-82646-2\u3002 \u30ad\u30fc\u30b9\u30fbO\u30fb\u30b2\u30c7\u30b9\u3001\u30b9\u30c6\u30a3\u30fc\u30d6\u30f3\u30fbR\u30fb\u30b6\u30dd\u30fc\u30eb\u3001\u30b8\u30e7\u30fc\u30b8\u30fb\u30e9\u30d0\u30fc\u30f3\uff1a \u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u30fc\u4ee3\u6570\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3002 Kluwer\u3001\u30dc\u30b9\u30c8\u30f3MA u\u3002 a\u3002 1992\u3001ISBN 0-7923-9259-0\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\/10573#breadcrumbitem","name":"ComputerLgebra-\u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2"}}]}]