{"id":1700,"date":"2019-10-30T09:16:18","date_gmt":"2019-10-30T01:16:18","guid":{"rendered":"http:\/\/www.xuehelp.cn\/?p=1700"},"modified":"2019-10-30T09:16:18","modified_gmt":"2019-10-30T01:16:18","slug":"%e5%8e%9f%e6%9d%a5%e5%a4%9a%e9%a1%b9%e5%bc%8f%e5%8f%af%e4%bb%a5%e7%94%a8%e6%9d%a5%e7%8e%a9%e6%b6%82%e8%89%b2%e6%b8%b8%e6%88%8f","status":"publish","type":"post","link":"http:\/\/www.xuehelp.cn\/index.php\/archives\/1700","title":{"rendered":"\u539f\u6765\u591a\u9879\u5f0f\u53ef\u4ee5\u7528\u6765\u73a9\u6d82\u8272\u6e38\u620f"},"content":{"rendered":"

\u00a0 $\"\"$ <\/p>\n

2015\u5e74\uff0c\u8bd7\u4eba\u6570\u5b66\u5bb6June Huh\u5e2e\u52a9\u89e3\u51b3\u4e86\u4e00\u4e2a50\u5e74\u524d\u7684\u95ee\u9898\u3002\u8fd9\u4e2a\u95ee\u9898\u662f\u5173\u4e8e\u4e00\u4e2a\u53eb\u505a\u201c\u62df\u9635\u201d(matroids)\u7684\u590d\u6742\u7684\u6570\u5b66\u5bf9\u8c61\uff0c\u5b83\u662f\u7531\u70b9\u3001\u7ebf\u548c\u56fe\u7247\u7684\u7ec4\u5408\u800c\u6210\u3002\u540c\u65f6\u5b83\u4e5f\u662f\u4e00\u4e2a\u5173\u4e8e\u591a\u9879\u5f0f\u7684\u95ee\u9898\u2014\u2014\u90a3\u4e9b\u6570\u5b66\u8bfe\u4e0a\u5e38\u89c1\u7684\u53ef\u4ee5\u628a\u53d8\u91cf\u6c42\u4e0d\u540c\u5e42\u6b21\u518d\u6c42\u548c\u7684\u8868\u8fbe\u5f0f\u3002<\/p>\n

\u6709\u65f6\u4f60\u53ef\u80fd\u5728\u5b66\u6821\u91cc\u9047\u5230\u591a\u9879\u5f0f\u7684\u5408\u5e76\u3001\u5206\u89e3\u548c\u7b80\u5316\u7684\u95ee\u9898\u3002\u4f8b\u5982\uff0c\u4f60\u4e5f\u8bb8\u8bb0\u5f97x<\/em>\u00b2<\/em>\u00a0\u00a0+ 2xy<\/em>\u00a0+\u00a0<\/span>y<\/em>\u00b2<\/em>\u00a0\u00a0= (x<\/em>\u00a0+\u00a0<\/span>y<\/em>)\u00b2<\/em>\u00a0\u3002\u8fd9\u662f\u4e00\u4e2a\u7b80\u6d01\u7684\u4ee3\u6570\u6280\u5de7\uff0c\u4f46\u662f\u5b83\u5230\u5e95\u6709\u4ec0\u4e48\u7528\u5904\uff1f\u591a\u9879\u5f0f\u64c5\u957f\u4e8e\u63ed\u793a\u9690\u85cf\u7ed3\u6784\uff0c\u8fd9\u4e2a\u4e8b\u5b9e\u5728Huh\u7684\u8bc1\u660e\u4e2d\u6709\u7740\u91cd\u8981\u7684\u4f5c\u7528\u3002\u4e0b\u9762\u8ba9\u6211\u4eec\u7528\u4e00\u4e2a\u7b80\u5355\u7684\u4f8b\u5b50\u6765\u8bf4\u660e\u5982\u4f55\u5b9e\u73b0\u8fd9\u4e00\u70b9\u3002<\/p>\n

\u5047\u8bbe\u8fd9\u91cc\u6709\u4e00\u4e2a\u6e38\u620f\u8981\u6c42\u5c06\u4e24\u7ec4\u73a9\u5bb6\u5b89\u6392\u5728\u4e00\u5f20\u65b9\u684c\u4e0a\u3002\u4e3a\u4e86\u9632\u6b62\u4ed6\u4eec\u4f5c\u5f0a\uff0c\u9700\u8981\u907f\u514d\u540c\u961f\u7684\u73a9\u5bb6\u5750\u5728\u76f8\u90bb\u7684\u5ea7\u4f4d\u4e0a\u3002\u90a3\u4e48\u4e00\u5171\u6709\u591a\u5c11\u79cd\u4e0d\u540c\u7684\u5b89\u6392\u65b9\u6cd5\uff1f<\/p>\n

\u6e38\u620f\u4e00\u5f00\u59cb\uff0c\u6211\u4eec\u5c06\u73a9\u5bb6\u5206\u4e3a\u7ea2\u8272\u548c\u84dd\u8272\u4e24\u79cd\u3002\u5982\u56fe\u6240\u793a\uff0c\u5047\u8bbe\u5148\u5c06\u4e00\u4e2a\u7ea2\u8272\u73a9\u5bb6\u5b89\u6392\u5728\u56fe\u7684\u4e0a\u9762\u7684\u4f4d\u7f6e\u3002<\/p>\n

\u00a0 $\"\"$ <\/p>\n

\u4e0a\u9762\u7684\u4f4d\u7f6e\u5de6\u53f3\u5404\u6709\u4e00\u4e2a\u76f8\u90bb\u7684\u5ea7\u4f4d\uff0c\u56e0\u6b64\uff0c\u4e3a\u4e86\u6ee1\u8db3\u6211\u4eec\u7684\u8981\u6c42\uff0c\u8fd9\u4e24\u4e2a\u5ea7\u4f4d\u5fc5\u987b\u90fd\u5b89\u6392\u7ed9\u84dd\u8272\u73a9\u5bb6\u3002<\/p>\n

\u00a0 $\"\"$ <\/p>\n

\u56fe\u7684\u5e95\u90e8\u8fd8\u5269\u4e0b\u4e86\u4e00\u4e2a\u548c\u4e24\u4e2a\u84dd\u8272\u73a9\u5bb6\u76f8\u90bb\u7684\u4f4d\u7f6e\uff0c\u6240\u4ee5\u5fc5\u987b\u6709\u4e00\u4e2a\u7ea2\u8272\u7684\u73a9\u5bb6\u5750\u5728\u90a3\u91cc\u3002<\/p>\n

\u00a0 $\"\"$ <\/p>\n

\u56e0\u4e3a\u6ca1\u6709\u4e00\u4e2a\u73a9\u5bb6\u5750\u5728\u4ed6\u961f\u53cb\u7684\u65c1\u8fb9\uff0c\u6211\u4eec\u7684\u9650\u5b9a\u7684\u6761\u4ef6\u6ee1\u8db3\u4e86\u3002<\/p>\n

\u6211\u4eec\u4e5f\u53ef\u4ee5\u5728\u6e38\u620f\u4e00\u5f00\u59cb\u7684\u65f6\u5019\u5c06\u4e00\u4e2a\u84dd\u8272\u73a9\u5bb6\u5b89\u6392\u5728\u4e0a\u9762\u3002\u548c\u4e0a\u6587\u76f8\u7c7b\u4f3c\u7684\u63a8\u7406\u53ef\u4ee5\u5f97\u5230\u4e0b\u9762\u7684\u5b89\u6392\u3002<\/p>\n

$\"\"$ <\/p>\n

\u540c\u6837\uff0c\u6ca1\u6709\u4e00\u4e2a\u73a9\u5bb6\u5750\u5728\u4ed6\u7684\u961f\u53cb\u7684\u65c1\u8fb9\u3002\u6211\u4eec\u7684\u7ea6\u675f\u6761\u4ef6\u6ee1\u8db3\u4e86\uff0c\u6240\u4ee5\u8fd9\u662f\u53e6\u4e00\u79cd\u53ef\u80fd\u7684\u5b89\u6392\u65b9\u6cd5\u3002\u4e8b\u5b9e\u4e0a\uff0c\u8fd9\u4e2a\u6e38\u620f\u53ea\u6709\u4e24\u79cd\u53ef\u80fd\u7684\u6392\u5ea7\u7ed3\u679c\u3002\u4e00\u65e6\u6211\u4eec\u9009\u5b9a\u4e86\u4e0a\u9762\u4f4d\u7f6e\u7684\u989c\u8272\uff0c\u5269\u4e0b\u5ea7\u4f4d\u7684\u989c\u8272\u4e5f\u90fd\u51b3\u5b9a\u597d\u4e86\u3002<\/p>\n

\u6709\u4e00\u79cd\u65b9\u6cd5\u80fd\u8ba9\u6211\u4eec\u4e0d\u7528\u753b\u51fa\u6240\u6709\u4e0d\u540c\u7684\u5ea7\u4f4d\u56fe\u5c31\u53ef\u4ee5\u77e5\u9053\u53ea\u6709\u4e24\u79cd\u5b89\u6392\u5ea7\u4f4d\u7684\u65b9\u6cd5\u3002\u8ba9\u6211\u4eec\u4ece\u4e0a\u9762\u5f00\u59cb\uff1a\u5bf9\u90a3\u4e2a\u5ea7\u4f4d\u6211\u4eec\u6709\u4e24\u79cd\u9009\u62e9\uff0c\u7ea2\u8272\u6216\u8005\u84dd\u8272\u3002\u5f53\u6211\u4eec\u505a\u51fa\u8fd9\u4e2a\u9009\u62e9\u7684\u65f6\u5019\uff0c\u5b83\u5de6\u8fb9\u548c\u53f3\u8fb9\u7684\u4f4d\u7f6e\u90fd\u53ea\u6709\u4e00\u79cd\u9009\u62e9\uff08\u53e6\u4e00\u79cd\u989c\u8272\uff09\u3002\u7136\u540e\uff0c\u5bf9\u6700\u4e0b\u9762\u7684\u5ea7\u4f4d\u6765\u8bf4\uff0c\u4e5f\u662f\u53ea\u6709\u4e00\u4e2a\u9009\u62e9\uff1a\u6211\u4eec\u5f00\u59cb\u6e38\u620f\u7684\u65f6\u5019\u9009\u62e9\u7684\u989c\u8272\u3002\u901a\u8fc7\u8fd0\u7528\u201c\u57fa\u672c\u8ba1\u7b97\u539f\u7406\u201d\uff0c\u6211\u4eec\u77e5\u9053\u6240\u6709\u53ef\u80fd\u6027\u7684\u4e2a\u6570\u662f\u6bcf\u4e00\u79cd\u9009\u62e9\u53ef\u80fd\u6027\u6570\u7684\u4e58\u79ef\u3002\u8fd9\u5c31\u5f97\u5230\u4e862 \u00d7 1 \u00d7 1 \u00d7 1 = 2\u4e00\u5171\u4e24\u4e2a\u5ea7\u4f4d\uff0c\u5c31\u50cf\u6211\u4eec\u7528\u56fe\u50cf\u7684\u786e\u5b9a\u51fa\u6765\u7684\u4e00\u6837\u3002<\/p>\n

\u73b0\u5728\uff0c\u6211\u4eec\u52a0\u5165\u7528\u5176\u4ed6\u989c\u8272\u8868\u793a\u7b2c\u4e09\u652f\u961f\u4f0d\u3002\u60f3\u8c61\u73b0\u5728\u6709\u7ea2\u8272\uff0c\u84dd\u8272\u548c\u9ec4\u8272\u4e09\u79cd\u73a9\u5bb6\u3002\u5982\u679c\u76f8\u90bb\u7684\u5ea7\u4f4d\u4e0d\u80fd\u5b89\u6392\u540c\u6837\u989c\u8272\u7684\u73a9\u5bb6\uff0c\u90a3\u4e48\u6709\u591a\u5c11\u79cd\u4e0d\u540c\u7684\u5b89\u6392\u65b9\u5f0f\uff1f\u753b\u51fa\u6240\u6709\u7684\u53ef\u80fd\u6027\u53ef\u80fd\u4f1a\u9700\u8981\u5f88\u591a\u7684\u56fe\u50cf\uff0c\u6240\u4ee5\u8ba9\u6211\u4eec\u6539\u7528\u8ba1\u7b97\u53c2\u6570\u8bd5\u8bd5\u3002<\/p>\n

\u73b0\u5728\u4e0a\u9762\u7684\u4f4d\u7f6e\u6709\u4e09\u79cd\u989c\u8272\u53ef\u4ee5\u9009\u62e9\u3002\u505a\u51fa\u9009\u62e9\u4e4b\u540e\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u4e3a\u5de6\u53f3\u4e24\u4e2a\u4f4d\u7f6e\u9009\u62e9\u5269\u4e0b\u4e24\u4e2a\u989c\u8272\u4e2d\u7684\u4efb\u610f\u4e00\u4e2a\u3002<\/p>\n

\u90a3\u4e48\u65b9\u684c\u4e0b\u65b9\u7684\u5ea7\u4f4d\u4f1a\u53d1\u751f\u4ec0\u4e48\uff1f\u4eba\u4eec\u5f88\u5bb9\u6613\u8bf4\u6700\u540e\u4e00\u4e2a\u4f4d\u7f6e\u53ea\u6709\u4e00\u79cd\u9009\u62e9\uff0c\u56e0\u4e3a\u5b83\u5de6\u53f3\u90fd\u6709\u76f8\u90bb\u7684\u5ea7\u4f4d\u3002\u4f46\u4f60\u6709\u6ca1\u6709\u53d1\u73b0\u5176\u4e2d\u7684\u95ee\u9898\uff1f<\/p>\n

\u00a0 $\"\"$ <\/p>\n

\u5982\u679c\u5de6\u53f3\u4e24\u8fb9\u4f4d\u7f6e\u989c\u8272\u4e0d\u540c\uff0c\u90a3\u4e0b\u9762\u7684\u4f4d\u7f6e\u786e\u5b9e\u53ea\u6709\u4e00\u79cd\u9009\u62e9\u3002\u4f8b\u5982\uff0c\u5de6\u8fb9\u662f\u84dd\u8272\u7684\uff0c\u53f3\u8fb9\u662f\u7ea2\u8272\u7684\uff0c\u90a3\u4e48\u5e95\u4e0b\u7684\u5c31\u5fc5\u987b\u662f\u9ec4\u8272\u7684\u3002\u4f46\u662f\u5de6\u53f3\u7684\u989c\u8272\u76f8\u540c\u53c8\u4f1a\u600e\u4e48\u6837\uff1f\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u5e95\u4e0b\u989c\u8272\u7684\u9009\u62e9\u4f1a\u6709\u4e24\u79cd\u3002\u6700\u540e\u7684\u9009\u62e9\u53d6\u51b3\u4e8e\u4e00\u5f00\u59cb\u7684\u9009\u62e9\uff0c\u8fd9\u5c31\u8ba9\u6211\u4eec\u7684\u8ba1\u7b97\u53d8\u5f97\u590d\u6742\u8d77\u6765\u3002<\/p>\n

\u56e0\u6b64\u6211\u4eec\u5fc5\u987b\u8003\u8651\u4e24\u79cd\u76f8\u4e92\u72ec\u7acb\u7684\u60c5\u51b5\uff1a\u5de6\u8fb9\u548c\u53f3\u8fb9\u989c\u8272\u76f8\u540c\u7684\u65f6\u5019\u548c\u5de6\u8fb9\u548c\u53f3\u8fb9\u989c\u8272\u4e0d\u76f8\u540c\u7684\u65f6\u5019\u3002<\/p>\n

\u5982\u679c\u5de6\u8fb9\u548c\u53f3\u8fb9\u7684\u989c\u8272\u76f8\u540c\uff0c\u90a3\u4e48\u6bcf\u6761\u8fb9\u989c\u8272\u7684\u53ef\u80fd\u6027\u5c31\u5982\u4e0b\u56fe\u6240\u793a\uff1a<\/p>\n

\u00a0 $\"\"$ <\/p>\n

\u9996\u5148\uff0c\u4e0a\u9762\u7684\u989c\u8272\u6709\u4e09\u79cd\u9009\u62e9\u3002\u7136\u540e\uff0c\u5bf9\u4e8e\u53f3\u8fb9\u7684\u989c\u8272\u8fd8\u5269\u4e86\u4e24\u79cd\u9009\u62e9\u3002\u56e0\u4e3a\u6211\u4eec\u5047\u8bbe\u5de6\u8fb9\u548c\u53f3\u8fb9\u989c\u8272\u662f\u4e00\u6837\u7684\uff0c\u6240\u4ee5\u5de6\u8fb9\u7684\u989c\u8272\u53ea\u6709\u4e00\u79cd\u53ef\u80fd\uff1a\u548c\u53f3\u8fb9\u7684\u989c\u8272\u76f8\u540c\u3002\u6700\u540e\uff0c\u56e0\u4e3a\u5de6\u8fb9\u548c\u53f3\u8fb9\u989c\u8272\u76f8\u540c\uff0c\u5e95\u4e0b\u7684\u989c\u8272\u53ef\u4ee5\u662f\u5269\u4e0b\u7684\u4e24\u79cd\u989c\u8272\u4e2d\u7684\u4efb\u610f\u4e00\u79cd\u3002\u8fd9\u6837\u6211\u4eec\u5c31\u6709 \u00a03 \u00d7 2 \u00d7 1 \u00d7 2 = 12\u79cd\u53ef\u80fd\u7684\u7ed3\u679c\u3002<\/p>\n

\u73b0\u5728\u8ba9\u6211\u4eec\u8003\u8651\u4e00\u4e0b\u5de6\u8fb9\u548c\u53f3\u8fb9\u989c\u8272\u4e0d\u540c\u65f6\u7684\u53ef\u80fd\u6027\uff1a<\/p>\n

\u00a0 $\"\"$ <\/p>\n

\u540c\u6837\uff0c\u4e0a\u9762\u6709\u4e09\u79cd\u9009\u62e9\u53f3\u8fb9\u6709\u4e24\u79cd\u9009\u62e9\u3002\u5de6\u8fb9\u4ecd\u7136\u53ea\u6709\u4e00\u79cd\u9009\u62e9\uff0c\u4f46\u662f\u8fd9\u6b21\u7684\u539f\u56e0\u548c\u7b2c\u4e00\u6b21\u7684\u4e0d\u540c\uff1a \u5b83\u65e2\u4e0d\u80fd\u548c\u76f8\u90bb\u7684\u4e0a\u9762\u989c\u8272\u76f8\u540c\uff0c\u53c8\u5f97\u7b26\u5408\u5047\u8bbe\u548c\u53f3\u8fb9\u989c\u8272\u4e0d\u540c\u3002\u800c\u56e0\u4e3a\u5de6\u8fb9\u548c\u53f3\u8fb9\u7684\u989c\u8272\u4e0d\u540c\uff0c\u4e0b\u9762\u7684\u989c\u8272\u53ea\u6709\u4e00\u79cd\u9009\u62e9\uff08\u548c\u4e0a\u9762\u4e00\u6837\u7684\u989c\u8272\uff09\u3002\u8fd9\u79cd\u60c5\u51b5\u67093 \u00d7 2 \u00d7 1 \u00d7 1 = 6\u79cd\u53ef\u80fd\u7684\u7ed3\u679c\u3002<\/p>\n

\u56e0\u4e3a\u8fd9\u4e24\u79cd\u60c5\u51b5\u5305\u542b\u4e86\u6240\u6709\u7684\u53ef\u80fd\uff0c\u6211\u4eec\u53ea\u9700\u8981\u628a\u5b83\u4eec\u52a0\u8d77\u6765\u5f97\u5230\u603b\u5171\u670912 + 6 = 18\u79cd\u53ef\u80fd\u7684\u7ed3\u679c\u3002<\/p>\n

\u589e\u52a0\u4e86\u4e00\u79cd\u989c\u8272\u8ba9\u6211\u4eec\u7684\u95ee\u9898\u53d8\u5f97\u590d\u6742\uff0c\u4f46\u662f\u6211\u4eec\u7684\u52aa\u529b\u4f1a\u5f97\u5230\u56de\u62a5\u3002\u6211\u4eec\u73b0\u5728\u53ef\u4ee5\u7528\u8fd9\u79cd\u65b9\u6cd5\u89e3\u51b34\uff0c5\u6216\u8005\u4efb\u610fq\u79cd\u4e0d\u540c\u989c\u8272\u65f6\u7684\u95ee\u9898\u3002<\/p>\n

\u65e0\u8bba\u5728\u591a\u5c11\u79cd\u989c\u8272\u4e2d\u8fdb\u884c\u9009\u62e9\uff0c\u6211\u4eec\u90fd\u8981\u8003\u8651\u4e24\u79cd\u60c5\u51b5\uff1a\u5de6\u8fb9\u548c\u53f3\u8fb9\u989c\u8272\u76f8\u540c\uff0c\u5de6\u8fb9\u548c\u53f3\u8fb9\u989c\u8272\u4e0d\u540c\u3002\u5047\u8bbe\u6211\u4eec\u9700\u8981\u5728q\u79cd\u4e0d\u540c\u7684\u989c\u8272\u79cd\u8fdb\u884c\u9009\u62e9\u3002\u4e0b\u9762\u7684\u56fe\u50cf\u8868\u793a\u7684\u662f\u5f53\u5de6\u53f3\u989c\u8272\u76f8\u540c\u65f6\u6bcf\u6761\u8fb9\u4e0d\u540c\u7684\u9009\u62e9\u6570\u91cf\uff1a<\/p>\n

$\"\"$ <\/p>\n

\u4e00\u5f00\u59cb\uff0c\u4e0a\u9762\u7684\u5ea7\u4f4d\u6709q\u79cd\u989c\u8272\u53ef\u4ee5\u9009\u62e9\uff0c\u53f3\u9762\u7684\u5ea7\u4f4d\u6709q-1\u79cd\u989c\u8272\u53ef\u4ee5\u9009\u62e9\u3002\u56e0\u4e3a\u6211\u4eec\u5047\u8bbe\u5de6\u8fb9\u548c\u53f3\u8fb9\u989c\u8272\u76f8\u540c\uff0c\u6240\u4ee5\u5de6\u8fb9\u53ea\u6709\u4e00\u79cd\u9009\u62e9\u3002\u8fd9\u6837\uff0c\u4e0b\u9762\u53ef\u4ee5\u9009\u62e9q-1\u79cd\u989c\u8272\uff0c\u5373\u9664\u4e86\u5de6\u53f3\u7684\u90a3\u79cd\u989c\u8272\u4e4b\u5916\u7684\u4efb\u4f55\u989c\u8272\u3002\u6839\u636e\u57fa\u672c\u7b97\u6570\u539f\u7406\u6211\u4eec\u4e00\u5171\u5f97\u5230\u4e86q<\/em>\u00a0\u00d7 (q<\/em>\u00a0\u2013 1)\u00a0\u00d7 1\u00a0\u00d7 (q<\/em>\u00a0\u2013 1) =\u00a0q<\/em>(q<\/em>\u00a0\u2013 1)\u00b2<\/em>\u79cd\u53ef\u80fd\u7684\u7ed3\u679c\u3002<\/p>\n

\u5982\u679c\u5de6\u53f3\u989c\u8272\u4e0d\u540c\uff0c\u6211\u4eec\u53ef\u4ee5\u50cf\u8fd9\u6837\u5217\u4e3e\u53ef\u80fd\u7684\u7ed3\u679c\uff1a<\/p>\n

\u00a0 $\"\"$ <\/p>\n

\u540c\u6837\uff0c\u4e0a\u9762\u7684\u5ea7\u4f4d\u6709q\u79cd\u989c\u8272\u53ef\u4ee5\u9009\u62e9\uff0c\u53f3\u8fb9\u7684\u5ea7\u4f4d\u6709q\u79cd\u989c\u8272\u53ef\u4ee5\u9009\u62e9\u3002\u73b0\u5728\uff0c\u5de6\u8fb9\u7684\u989c\u8272\u4e0d\u80fd\u548c\u53f3\u8fb9\u7684\u989c\u8272\u76f8\u540c\uff0c\u6240\u4ee5\u6211\u4eec\u6709q-2\u79cd\u9009\u62e9\u3002\u5e95\u4e0b\u5ea7\u4f4d\u53ef\u4ee5\u662f\u9664\u4e86\u5de6\u53f3\u4e24\u79cd\u4e0d\u540c\u989c\u8272\u4e4b\u5916\u7684\u4efb\u610f\u989c\u8272\uff0c\u540c\u6837\u4e5f\u662f\u6709q-2\u79cd\u4e0d\u540c\u7684\u989c\u8272\u3002\u8fd9\u6837\u6211\u4eec\u4e00\u5171\u6709q<\/em>\u00a0\u00d7 (q<\/em>\u00a0\u2013 1)\u00a0\u00d7 (q<\/em>\u00a0\u2013 2)\u00a0\u00d7 (q<\/em>\u00a0\u2013 2) =\u00a0q<\/em>(q<\/em>\u00a0\u2013 1)(q<\/em>\u00a0\u2013 2)\u00b2<\/em>\u79cd\u53ef\u80fd\u7684\u7ed3\u679c\u3002\u56e0\u4e3a\u8fd9\u4e24\u79cd\u60c5\u51b5\u5305\u62ec\u4e86\u6240\u6709\u7684\u53ef\u80fd\u6027\uff0c\u6211\u4eec\u50cf\u524d\u9762\u4e00\u6837\u628a\u5b83\u4eec\u52a0\u5728\u4e00\u8d77\u5f97\u5230\u6700\u540e\u53ef\u80fd\u7ed3\u679c\u7684\u603b\u6570\uff1aq<\/em>(q<\/em>\u00a0\u2013 1)\u00b2<\/em>+\u00a0q<\/em>(q<\/em>\u00a0\u2013 1)(q<\/em>\u00a0\u2013 2)\u00b2<\/em>\u3002<\/p>\n

\u8fd9\u4e2a\u8868\u8fbe\u5f0f\u770b\u8d77\u6765\u597d\u50cf\u548c\u201c\u6211\u4eec\u80fd\u6709\u591a\u5c11\u79cd\u4e0d\u540c\u7684\u65b9\u5f0f\u8ba9\u4e0d\u540c\u7684\u961f\u5750\u5728\u65b9\u684c\u4e0a\uff0c\u540c\u65f6\u4e0d\u8ba9\u4e24\u4e2a\u961f\u53cb\u5750\u5728\u4e00\u8d77\u201d\u8fd9\u4e2a\u95ee\u9898\u6beb\u65e0\u5173\u7cfb\u3002\u4f46\u662f\u8fd9\u4e2a\u591a\u9879\u5f0f\u8868\u8fbe\u4e86\u5173\u4e8e\u8fd9\u4e2a\u95ee\u9898\u7684\u597d\u591a\u4fe1\u606f\u3002\u5b83\u4e0d\u5355\u544a\u8bc9\u4e86\u6211\u4eec\u5177\u4f53\u7684\u6570\u5b57\u7ed3\u679c\uff0c\u8fd8\u8868\u73b0\u51fa\u9690\u85cf\u5728\u8fd9\u9053\u9898\u4e4b\u4e0b\u7684\u4e00\u4e9b\u7ed3\u6784\u3002<\/p>\n

\u8fd9\u4e2a\u7279\u522b\u7684\u591a\u9879\u5f0f\u88ab\u79f0\u4e3a\u201c\u67d3\u8272\u591a\u9879\u5f0f\u201d(chromatic polynomial)\uff0c\u56e0\u4e3a\u5b83\u56de\u7b54\u4e86\u4e0b\u8ff0\u95ee\u9898\uff1a\u4f60\u6709\u591a\u5c11\u79cd\u4e0d\u540c\u7684\u65b9\u6cd5\u80fd\u591f\u7ed9\u7f51\u683c\uff08\u6216\u56fe\uff09\u7684\u65b9\u683c\u6216\u8005\u8282\u70b9\u4e0a\u8272\u4f7f\u5176\u4e0e\u76f8\u90bb\u7684\u65b9\u683c\u6216\u8282\u70b9\u989c\u8272\u4e0d\u540c\u3002<\/p>\n

\u6211\u4eec\u7684\u95ee\u9898\u6700\u521d\u662f\u5173\u4e8e\u7ed9\u961f\u4f0d\u5728\u4e00\u5f20\u684c\u5b50\u4e0a\u5b89\u6392\u5ea7\u4f4d\uff0c\u4f46\u662f\u6211\u4eec\u53ef\u4ee5\u5f88\u5bb9\u6613\u5730\u628a\u5b83\u8f6c\u5316\u6210\u4e00\u4e2a\u5173\u4e8e\u7ed9\u56fe\u50cf\u4e0a\u8282\u70b9\u4e0a\u8272\u7684\u95ee\u9898\u3002\u6211\u4eec\u4e0d\u518d\u60f3\u8c61\u4eba\u4eec\u56f4\u7740\u684c\u5b50\u5750\uff0c\u6211\u4eec\u5c06\u4eba\u4eec\u6bd4\u4f5c\u8282\u70b9\uff0c\u5982\u679c\u4ed6\u4eec\u5750\u5728\u4e00\u8d77\u5c31\u7528\u4e00\u6761\u7ebf\u628a\u4ed6\u4eec\u8fde\u63a5\u8d77\u6765\u3002<\/p>\n

\u00a0 $\"\"$ <\/p>\n

$\"\"$ <\/p>\n

\u73b0\u5728\uff0c\u56fe\u50cf\u4e2d\u7684\u6bcf\u4e00\u4e2a\u8282\u70b9\u7684\u989c\u8272\u53ef\u4ee5\u88ab\u770b\u6210\u65b9\u684c\u5468\u56f4\u7684\u4e00\u4e2a\u5ea7\u4f4d\uff0c\u800c\u201c\u90bb\u5ea7\u201d\u5728\u56fe\u4e0a\u53d8\u6210\u4e86\u201c\u6709\u4e00\u6761\u7ebf\u6bb5\u5c06\u5b83\u4eec\u8fde\u63a5\u8d77\u6765\u201d \u3002<\/p>\n

$\"\"$ <\/p>\n

\u65e2\u7136\u6211\u4eec\u5df2\u7ecf\u5c06\u6211\u4eec\u7684\u95ee\u9898\u7528\u4e00\u4e2a\u56fe\u8868\u793a\u51fa\u6765\uff0c\u90a3\u4e48\u8ba9\u6211\u4eec\u56de\u5230\u5b83\u7684\u67d3\u8272\u4e0d\u7b49\u5f0f\u3002\u4ee5\u4e0b\u6211\u4eec\u5c06\u6210\u5b83\u4e3aP<\/em>(q<\/em>)\u3002<\/p>\n

P<\/em>(q<\/em>) =\u00a0q<\/em>(q<\/em>\u00a0\u2013 1)\u00b2<\/em>\u00a0+\u00a0q<\/em>(q<\/em>\u00a0\u2013 1)(q<\/em>\u00a0\u2013 2)\u00b2<\/em><\/p>\n

\u8fd9\u4e2a\u591a\u9879\u5f0f\u7684\u597d\u5904\u662f\u5b83\u80fd\u591f\u56de\u7b54\u6211\u4eec\u6240\u6709\u53ef\u80fd\u7684\u56fe\u50cf\u4e0a\u8272\u95ee\u9898\u3002<\/p>\n

\u4f8b\u5982\uff1a\u4e3a\u4e86\u5f97\u5230\u6709\u4e09\u4e2a\u989c\u8272\u7684\u9898\u7684\u7b54\u6848\uff0c\u6211\u4eec\u8ba9q=3\uff0c\u4ece\u800c\u5f97\u5230\uff1a<\/p>\n

P<\/em>(3) = 3(3 \u2013 1)\u00b2<\/em>+ 3(3 \u2013 1)(3 \u2013 2)\u00b2<\/em>= 3 \u00d7 2\u00b2<\/em>\u00a0+ 3 \u00d7 2 \u00d7 1\u00b2<\/em>\u00a0= 12 + 6 = 18<\/p>\n

\u8fd9\u4e2a\u6070\u6070\u662f\u5728\u6211\u4eec\u4e0a\u9762\u7684\u4e09\u4e2a\u961f\u4f0d\u7684\u60c5\u51b5\u4e0b\u627e\u5230\u7684\u7b54\u6848\u3002\u800c\u5f53\u6211\u4eec\u8ba9q=2\u65f6\uff1a<\/p>\n

P<\/em>(2) =\u00a02(2 \u2013 1)\u00b2<\/em>\u00a0+ 2(2 \u2013 1)(2 \u2013 2)\u00b2<\/em>\u00a0= 2\u00a0\u00d7 1\u00b2<\/em>+ 2\u00a0\u00d7 1\u00a0\u00d7 0\u00b2<\/em>\u00a0= 2 + 0 = 2<\/p>\n

\u770b\u8d77\u6765\u662f\u4e0d\u662f\u5f88\u719f\u6089\uff1f\u8fd9\u662f\u6211\u4eec\u4e00\u5f00\u59cb\u4e24\u4e2a\u4e0d\u540c\u961f\u4f0d\u7684\u60c5\u51b5\u4e0b\u65f6\u7684\u7b54\u6848\u3002\u6211\u4eec\u53ea\u9700\u8981\u7ed9q\u4ee3\u5165\u9002\u5f53\u7684\u503c\u5c31\u80fd\u591f\u5f97\u5230\u6709\u56db\u4e2a\uff0c\u4e94\u4e2a\u751a\u81f3\u662f\u5341\u4e2a\u4e0d\u540c\u961f\u4f0d\u60c5\u51b5\u4e0b\u7684\u7b54\u6848\uff1aP<\/em>(4) = 84,\u00a0P<\/em>(5) = 260\u00a0and\u00a0<\/span>P<\/em>(10) = 6,570\u3002\u8272\u591a\u9879\u5f0f\u901a\u8fc7\u5f52\u7eb3\u6211\u4eec\u7684\u7b97\u6570\u65b9\u6cd5\uff0c\u5df2\u7ecf\u6355\u6349\u5230\u4e86\u8fd9\u4e2a\u95ee\u9898\u7684\u4e00\u4e9b\u57fa\u7840\u7ed3\u6784\u3002<\/p>\n

\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u5bf9\u591a\u9879\u5f0fP<\/em>(q<\/em>)\u505a\u4e00\u4e9b\u57fa\u672c\u7684\u4ee3\u6570\u8fd0\u7b97\u63ed\u9732\u66f4\u591a\u7684\u7ed3\u6784<\/p>\n

P<\/em>(q<\/em>) =\u00a0q<\/em>(q\u00a0\u2013<\/em>\u00a01)\u00b2<\/em>\u00a0+\u00a0q<\/em>(q \u2013\u00a0<\/em>1)(q\u00a0\u2013\u00a0<\/em>2)\u00b2<\/em>:<\/p>\n

=q<\/em>(q<\/em>\u22121)(q<\/em>\u22121)+q<\/em>(q<\/em>\u22121)(q<\/em>\u22122)\u00b2<\/p>\n

=q<\/em>(q<\/em>\u22121)((q<\/em>\u22121)+(q<\/em>\u22122)\u00b2)<\/p>\n

=q<\/em>(q<\/em>\u22121)(q<\/em>\u22121+q<\/em>\u00b2<\/em>\u22124q<\/em>+4)<\/p>\n

=q<\/em>(q<\/em>\u22121)(q<\/em>\u00b2<\/em>\u22123q<\/em>+3)<\/p>\n

\u8fd9\u91cc\u6211\u4eec\u5df2\u7ecf\u628aq<\/em>(q<\/em>\u00a0\u2013 1)\u4ece\u548c\u4e2d\u7684\u6bcf\u4e00\u4e2a\u90e8\u5206\u63d0\u53d6\u4e86\u51fa\u6765\u7136\u540e\u5408\u5e76\u540c\u7c7b\u9879\uff0c\u628a\u591a\u9879\u5f0f\u53d8\u6210\u7528\u4e58\u79ef\u8868\u793a\u51fa\u6765\u7684\u201c\u56e0\u5b50\u5f62\u5f0f\u201d\u3002\u5728\u56e0\u5b50\u5f62\u5f0f\u4e2d\uff0c\u4e00\u4e2a\u591a\u9879\u5f0f\u53ef\u4ee5\u901a\u8fc7\u5b83\u7684\u201c\u6839\u201d\u6765\u544a\u8bc9\u6211\u4eec\u7ed3\u6784\u3002<\/p>\n

\u4e00\u4e2a\u591a\u9879\u5f0f\u7684\u8ddf\u6307\u7684\u662f\u4f7f\u5f97\u591a\u9879\u5f0f\u4e3a0\u7684\u53bb\u503c\u3002\u5e76\u4e14\u4e00\u4e2a\u591a\u9879\u5f0f\u7684\u56e0\u5b50\u5f62\u5f0f\u4f7f\u5f97\u6c42\u6839\u53d8\u5f97\u5bb9\u6613\uff1a\u56e0\u4e3a\u591a\u9879\u5f0f\u662f\u4ee5\u56e0\u5f0f\u4e58\u79ef\u7684\u5f62\u5f0f\u5b58\u5728\u7684\uff0c\u4efb\u4f55\u8ba9\u5176\u4e2d\u4e00\u4e2a\u56e0\u5b50\u4e3a\u96f6\u90fd\u4f1a\u8ba9\u6574\u4e2a\u4e58\u79ef\u53d8\u4e3a\u96f6\uff0c\u56e0\u6b64\u591a\u9879\u5f0f\u4e5f\u662f0\u3002<\/p>\n

\u4f8b\u5982\uff0c\u6211\u4eec\u7684\u591a\u9879\u5f0fP<\/em>(q<\/em>) =\u00a0q<\/em>(q\u00a0<\/em>\u2013 1)(q<\/em>\u00b2<\/em>\u00a0\u2013 3q<\/em>\u00a0+ 3)\u6709\u4e00\u4e2a\u56e0\u5b50(q<\/em>\u00a0\u2013 1)\u3002\u5982\u679c\u6211\u4eec\u8ba9q=1\uff0c\u8fd9\u4e2a\u56e0\u5f0f\u5c31\u53d8\u6210\u4e860\uff0c\u4ece\u800c\u5c06\u6574\u4e2a\u5f0f\u5b50\u53d8\u6210\u4e860\u3002\u5c31\u662fP<\/em>(1) = 1(1 \u2013 1)(1^{2<\/sup>\u00a0\u2013 3 \u00d7 1 + 3) = 1 \u00d7 0 \u00d7 1 = 0. Similarly,\u00a0<\/span>P<\/em>(0) = 0\u00a0\u00d7 (\u20131)\u00a0\u00d7 3 = 0\u3002\u6240\u4ee5q=1\u548cq=0\u5c31\u662f\u6211\u4eec\u591a\u9879\u5f0f\u7684\u4e24\u4e2a\u6839\u3002\uff08\u4f60\u4e5f\u8bb8\u5728\u8003\u8651(q<\/em>^{2<\/sup>\u00a0\u2013 3q<\/em>\u00a0+ 3)\u7684\u95ee\u9898\u3002\u56e0\u4e3a\u6ca1\u6709\u4e00\u4e2a\u5b9e\u6570\u80fd\u8ba9\u8fd9\u4e2a\u56e0\u5f0f\u53d8\u4e3a0\uff0c\u6240\u4ee5\u5b83\u6ca1\u6709\u7ed9\u6211\u4eec\u7684\u8272\u591a\u9879\u5f0f\u63d0\u4f9b\u4efb\u4f55\u5b9e\u6839\u3002\uff09<\/p>\n}}

\u8fd9\u4e9b\u4ee3\u6570\u6839\u5728\u6211\u4eec\u7684\u56fe\u50cf\u4e2d\u662f\u6709\u610f\u4e49\u7684\u3002\u5982\u679c\u6211\u4eec\u53ea\u80fd\u9009\u62e9\u4e00\u79cd\u989c\u8272\uff0c\u90a3\u4e48\u6bcf\u4e00\u4e2a\u8282\u70b9\u90fd\u4f1a\u662f\u76f8\u540c\u7684\u989c\u8272\u3002\u90a3\u4e48\u7531\u4e8e\u76f8\u90bb\u7684\u4e24\u4e2a\u8282\u70b9\u4e0d\u80fd\u662f\u76f8\u540c\u7684\u989c\u8272\uff0c\u6211\u4eec\u65e0\u6cd5\u7ed9\u8fd9\u4e2a\u56fe\u50cf\u4e0a\u8272\u3002\u4f46\u662f\u8fd9\u5c31\u662fq<\/em>\u00a0= 1\u662f\u8fd9\u4e2a\u8272\u591a\u9879\u5f0f\u7684\u6839\u7684\u542b\u4e49\u3002\u5982\u679cP<\/em>(1) = 0\uff0c\u90a3\u4e48\u5c31\u6ca1\u6709\u529e\u6cd5\u80fd\u5728\u7ed9\u56fe\u50cf\u4e0a\u8272\u7684\u540c\u65f6\u4fdd\u8bc1\u76f8\u90bb\u7684\u8282\u70b9\u989c\u8272\u4e0d\u540c\u3002\u5982\u679c\u6211\u4eec\u67090\u79cd\u989c\u8272\u4f9b\u6211\u4eec\u9009\u62e9\uff1a\u00a0P<\/em>(0) = 0\uff0c\u7ed3\u679c\u4e5f\u662f\u540c\u6837\u7684\u3002\u67d3\u8272\u591a\u9879\u5f0f\u7684\u6839\u544a\u8bc9\u4e86\u6211\u4eec\u56fe\u7684\u7ed3\u6784\u3002<\/p>\n

\u5f53\u6211\u4eec\u5f00\u59cb\u770b\u5176\u4ed6\u56fe\u50cf\u7684\u65f6\u5019\uff0c\u4ece\u4ee3\u6570\u7684\u89d2\u5ea6\u770b\u8fd9\u4e2a\u7ed3\u6784\u7684\u80fd\u529b\u5c31\u53d8\u5f97\u66f4\u52a0\u91cd\u8981\u4e86\u3002\u8ba9\u6211\u4eec\u6765\u770b\u770b\u4e0b\u9762\u7684\u4e09\u89d2\u56fe\u50cf\u3002<\/p>\n

\u00a0 $\"\"$ <\/p>\n

\u7528q\u79cd\u989c\u8272\u7ed9\u4e0a\u9762\u7684\u56fe\u50cf\u4e0a\u8272\u6709\u591a\u5c11\u79cd\u65b9\u6cd5\u53ef\u4ee5\u4f7f\u4efb\u4f55\u76f8\u90bb\u7684\u4e24\u4e2a\u8282\u70b9\u989c\u8272\u4e0d\u540c\uff1f<\/p>\n

\u901a\u5e38\uff0c\u524d\u4e24\u4e2a\u8282\u70b9\u6709\u5206\u522b\u6709q\u548cq-1\u79cd\u9009\u62e9\u3002\u56e0\u4e3a\u5269\u4e0b\u7684\u8282\u70b9\u662f\u548c\u524d\u4e24\u4e2a\u90fd\u76f8\u90bb\u7684\uff0c\u6240\u4ee5\u5b83\u7684\u989c\u8272\u5fc5\u987b\u548c\u524d\u4e24\u4e2a\u7684\u989c\u8272\u90fd\u4e0d\u76f8\u540c\uff0c\u5c31\u53ea\u5269\u4e0b\u4e86q-2\u79cd\u9009\u62e9\u3002\u6240\u4ee5\u8fd9\u4e2a\u4e09\u89d2\u56fe\u50cf\u5bf9\u5e94\u7684\u8272\u591a\u9879\u5f0f\u5c31\u662f\uff1aP<\/em>(q<\/em>) =\u00a0q<\/em>(q<\/em>\u00a0\u2013 1)(q<\/em>\u00a0\u2013 2)\u3002<\/p>\n

\u5728\u5b83\u7684\u56e0\u5f0f\u5f62\u5f0f\u4e2d\uff0c\u8fd9\u4e2a\u8272\u591a\u9879\u5f0f\u544a\u8bc9\u4e86\u6211\u4eec\u4e00\u4e9b\u6709\u8da3\u7684\u4e8b\u60c5\uff1aq=2\u662f\u4e00\u4e2a\u6839\u3002\u800c\u4e14\u5982\u679cP<\/em>(2) = 0\uff0c\u6211\u4eec\u65e0\u6cd5\u7528\u4e24\u79cd\u989c\u8272\u7ed9\u8fd9\u4e2a\u56fe\u50cf\u4e0a\u8272\u7684\u540c\u65f6\u4fdd\u8bc1\u76f8\u90bb\u7684\u4e24\u4e2a\u8282\u70b9\u989c\u8272\u4e0d\u540c\u3002<\/p>\n

\u90a3\u4e48\uff0c\u60f3\u8c61\u4e00\u4e0b\u6cbf\u7740\u8fd9\u4e2a\u4e09\u89d2\u5f62\u7684\u5faa\u73af\u8d70\uff0c\u4f60\u6bcf\u8d70\u5230\u4e00\u4e2a\u8282\u70b9\uff0c\u5c31\u7ed9\u5b83\u6d82\u4e0a\u989c\u8272\u3002\u56e0\u4e3a\u4f60\u53ea\u6709\u4e24\u79cd\u989c\u8272\u53ef\u4ee5\u9009\u62e9\uff0c\u90a3\u4f60\u53ea\u80fd\u6bcf\u8d70\u5230\u4e00\u4e2a\u8282\u70b9\u5c31\u53d8\u6362\u4e00\u79cd\u989c\u8272\uff1a\u5982\u679c\u7b2c\u4e00\u4e2a\u662f\u7ea2\u8272\uff0c\u90a3\u4e48\u7b2c\u4e8c\u4e2a\u5c31\u5fc5\u987b\u662f\u84dd\u8272\uff0c\u8fd9\u4e5f\u4ee3\u8868\u7740\u7b2c\u4e09\u4e2a\u5fc5\u987b\u662f\u7ea2\u8272\u3002\u4f46\u662f\u7b2c\u4e00\u4e2a\u548c\u7b2c\u4e09\u4e2a\u662f\u76f8\u90bb\u7684\uff0c\u6240\u4ee5\u5b83\u4eec\u4e0d\u80fd\u90fd\u662f\u7ea2\u8272\u7684\u3002\u6b63\u5982\u591a\u9879\u5f0f\u9884\u6d4b\u7684\u4e00\u6837\uff0c\u4e24\u79cd\u989c\u8272\u662f\u4e0d\u591f\u7684\u3002<\/p>\n

\u4f7f\u7528\u8fd9\u79cd\u65b9\u6cd5\u4ea4\u66ff\u8bba\u8bc1\uff0c\u4f60\u53ef\u4ee5\u63a8\u5bfc\u51fa\u4e00\u4e2a\u6709\u529b\u7684\u7ed3\u8bba\uff1a\u4efb\u4f55\u6709\u5947\u6570\u4e2a\u8282\u70b9\u7684\u5faa\u73af\u7684\u8272\u591a\u9879\u5f0f\u90fd\u5fc5\u987b\u67092\u4f5c\u4e3a\u4e00\u4e2a\u6839\u3002\u8fd9\u662f\u56e0\u4e3a\u5982\u679c\u4f60\u5728\u4e00\u4e2a\u6709\u5947\u6570\u4e2a\u8282\u70b9\u7684\u5faa\u73af\u4e2d\u4ea4\u66ff\u4f7f\u7528\u4e24\u79cd\u989c\u8272\uff0c\u4f60\u5c31\u4f1a\u7ed9\u7b2c\u4e00\u4e2a\u548c\u6700\u540e\u4e00\u4e2a\u6d82\u4e0a\u4e00\u6837\u7684\u989c\u8272\u3002\u4f46\u662f\u56e0\u4e3a\u5b83\u662f\u4e00\u4e2a\u5faa\u73af\uff0c\u7b2c\u4e00\u4e2a\u548c\u6700\u540e\u4e00\u4e2a\u662f\u76f8\u90bb\u7684\u3002\u8fd9\u5c31\u662f\u4e0d\u53ef\u80fd\u6ee1\u8db3\u6761\u4ef6\u7684\u4e86\u3002<\/p>\n

\u4f8b\u5982\uff0c\u6211\u4eec\u53ef\u4ee5\u7528\u5404\u79cd\u6280\u5de7\u786e\u5b9a\u4e00\u4e2a\u6709\u4e94\u4e2a\u8282\u70b9\u7684\u5faa\u73af\u6240\u5bf9\u5e94\u7684\u8272\u591a\u9879\u5f0f\u4e3aP<\/em>(q<\/em>) =\u00a0q<\/em>^{5<\/sup>\u00a0\u2013 5q<\/em>^{4<\/sup>\u00a0+ 10q<\/em>^{3<\/sup>\u00a0\u2013 10q<\/em>^{2<\/sup>\u00a0+ 4q<\/em>\u3002\u4f46\u5f53\u6211\u4eec\u628a\u5b83\u53d8\u6362\u4e3a\u56e0\u5f0f\u5f62\u5f0f\u7684\u65f6\u5019\uff0c\u5b83\u5c31\u53d8\u6210\u4e86P<\/em>(q<\/em>) =\u00a0q<\/em>(q\u00a0<\/em>\u2013 1)(q\u00a0<\/em>\u2013 2)(q<\/em>^{2<\/sup>\u00a0\u2013 2q<\/em>\u00a0+ 2)\u3002\u5c31\u50cf\u6211\u4eec\u731c\u6d4b\u7684\u90a3\u6837\uff0c\u6211\u4eec\u770b\u89c1q<\/em>\u00a0= 2\u662f\u4e00\u4e2a\u6839\u4e5f\u5c31\u662fP<\/em>(2) = 0\u3002\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u4e00\u65e6\u6211\u4eec\u5efa\u7acb\u8d77\u4e86\u56fe\u50cf\u548c\u5bf9\u5e94\u7684\u591a\u9879\u5f0f\u4e4b\u95f4\u7684\u8054\u7cfb\uff0c\u6211\u4eec\u5c31\u4f1a\u53d1\u73b0\uff1a\u591a\u9879\u5f0f\u53ef\u4ee5\u544a\u8bc9\u6211\u4eec\u56fe\u7684\u7ed3\u6784\uff0c\u56fe\u4e5f\u53ef\u4ee5\u544a\u8bc9\u6211\u4eec\u5b83\u4eec\u6240\u5bf9\u5e94\u7684\u591a\u9879\u5f0f\u7684\u7ed3\u6784\u3002<\/p>\n}}}}}

\u6b63\u662f\u5bf9\u7ed3\u6784\u7684\u7814\u7a76\u8ba9June Huh\u8bc1\u660e\u4e86Read\u572840\u5e74\u524d\u5173\u4e8e\u67d3\u8272\u591a\u9879\u5f0f\u7684\u731c\u60f3\u3002\u8fd9\u4e2a\u731c\u60f3\u662f\u8bf4\u5f53\u6211\u4eec\u6309\u987a\u5e8f\u5217\u51fa\u4e00\u4e2a\u8272\u591a\u9879\u5f0f\u7684\u7cfb\u6570\u5e76\u4e14\u5ffd\u7565\u5b83\u4eec\u7684\u7b26\u53f7\u7684\u65f6\u5019\uff0c\u5c31\u6ee1\u8db3\u4e86\u4e00\u4e2a\u7279\u6b8a\u60c5\u51b5\uff1a\u4e5f\u5c31\u662f\uff0c\u4efb\u4f55\u4e00\u4e2a\u7cfb\u6570\u7684\u5e73\u65b9\u90fd\u5fc5\u7136\u5927\u4e8e\u7b49\u4e8e\u4e0e\u5b83\u76f8\u90bb\u7684\u4e24\u4e2a\u7cfb\u6570\u7684\u4e58\u79ef\u3002\u4f8b\u5982\uff1a\u5728\u6709\u4e94\u4e2a\u8282\u70b9\u7684\u5faa\u73af\u6240\u5bf9\u5e94\u7684\u8272\u591a\u9879\u5f0f\u4e2d\uff0cP<\/em>(q<\/em>)\u00a0<\/span>\u00a0= q^5 -5q^4 +10q\u00b3- 10q\u00b2 +4q<\/em>\uff0c<\/em>\u6211\u4eec\u53ef\u4ee5\u53d1\u73b05^{2<\/sup>\u00a0\u2265\u00a01 \u00d7 10, 10^{2<\/sup>\u00a0\u2265\u00a05\u00a0\u00d7 10\u4ee5\u53ca\u00a010^{2<\/sup>\u00a0\u2265\u00a010 \u00d7 4\u3002\u8fd9\u8bf4\u660e\u5e76\u4e0d\u662f\u6bcf\u4e00\u4e2a\u591a\u9879\u5f0f\u90fd\u662f\u4e00\u4e2a\u8272\u591a\u9879\u5f0f\uff1a\u67d3\u8272\u591a\u9879\u5f0f\u901a\u8fc7\u548c\u56fe\u50cf\u7684\u8fde\u63a5\u6709\u7740\u66f4\u6df1\u7684\u7ed3\u6784\u3002\u66f4\u91cd\u8981\u7684\u662f\uff0c\u8fd9\u4e9b\u591a\u9879\u5f0f\u548c\u5176\u4ed6\u9886\u57df\u76f4\u63a5\u7684\u5173\u7cfb\u8ba9Huh\u548c\u4ed6\u7684\u5408\u4f5c\u8005\u5728\u8bc1\u660e\u4e86Read\u7684\u731c\u60f3\u51e0\u5e74\u540e\u89e3\u51b3\u4e86\u4e00\u4e2a\u66f4\u52a0\u5e7f\u6cdb\u7684\u5f00\u653e\u6027\u95ee\u9898\u2014\u2014\u7f57\u5854\u731c\u60f3(Rota)\u3002<\/p>\n}}}

\u5927\u5bb6\u90fd\u77e5\u9053\u591a\u9879\u5f0f\u6ca1\u5565\u4e86\u4e0d\u8d77\u7684\uff1a\u4e0d\u8fc7\u5c31\u662f\u7528\u7b26\u53f7\u6765\u62bd\u8c61\u8868\u793a\u7684\u4e00\u4e9b\u8fd0\u7b97\u800c\u5df2\u3002\u4f46\u662f\u591a\u9879\u5f0f\u4ee5\u53ca\u591a\u9879\u5f0f\u7684\u7279\u5f81\u2014\u2014\u5b83\u4eec\u7684\u6839\uff0c\u5b83\u4eec\u7684\u7cfb\u6570\uff0c\u5b83\u4eec\u5404\u79cd\u5404\u6837\u7684\u5f62\u5f0f\u2014\u2014\u80fd\u591f\u5e2e\u52a9\u6211\u4eec\u5728\u4ee4\u4eba\u60ca\u5947\u7684\u5730\u65b9\u63ed\u793a\u7ed3\u6784\uff0c\u5efa\u7acb\u4e86\u6211\u4eec\u65e5\u5e38\u751f\u6d3b\u548c\u4ee3\u6570\u4e4b\u95f4\u7684\u8054\u7cfb\u3002<\/p>\n

\n","protected":false},"excerpt":{"rendered":"

\u591a\u9879\u5f0f\u4e0d\u4ec5\u662f\u8bfe\u672c\u4e0a\u62bd\u8c61\u7684\u7ec3\u4e60\u9898\u3002\u5b83\u4eec\u8fd8\u6709\u52a9\u4e8e\u5728\u4e00\u4e9b\u4ee4\u4eba\u610f\u60f3\u4e0d\u5230\u7684\u5730\u65b9\u63ed\u793a\u6570\u5b66\u7ed3\u6784\u3002<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[402],"tags":[567],"_links":{"self":[{"href":"http:\/\/www.xuehelp.cn\/index.php\/wp-json\/wp\/v2\/posts\/1700"}],"collection":[{"href":"http:\/\/www.xuehelp.cn\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.xuehelp.cn\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.xuehelp.cn\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.xuehelp.cn\/index.php\/wp-json\/wp\/v2\/comments?post=1700"}],"version-history":[{"count":1,"href":"http:\/\/www.xuehelp.cn\/index.php\/wp-json\/wp\/v2\/posts\/1700\/revisions"}],"predecessor-version":[{"id":1701,"href":"http:\/\/www.xuehelp.cn\/index.php\/wp-json\/wp\/v2\/posts\/1700\/revisions\/1701"}],"wp:attachment":[{"href":"http:\/\/www.xuehelp.cn\/index.php\/wp-json\/wp\/v2\/media?parent=1700"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.xuehelp.cn\/index.php\/wp-json\/wp\/v2\/categories?post=1700"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.xuehelp.cn\/index.php\/wp-json\/wp\/v2\/tags?post=1700"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}