{"id":174174,"date":"2024-05-08T18:26:31","date_gmt":"2024-05-08T10:26:31","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/174174.html"},"modified":"2024-05-08T18:26:44","modified_gmt":"2024-05-08T10:26:44","slug":"%e5%a6%82%e4%bd%95%e7%94%a8python%e5%ae%9e%e7%8e%b0%e5%9b%a0%e5%bc%8f%e5%88%86%e8%a7%a3%e5%8a%9f%e8%83%bd","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/174174.html","title":{"rendered":"\u5982\u4f55\u7528Python\u5b9e\u73b0\u56e0\u5f0f\u5206\u89e3\u529f\u80fd"},"content":{"rendered":"<p style=\"text-align:center\"><img decoding=\"async\" src=\"https:\/\/cdn-kb.worktile.com\/kb\/wp-content\/uploads\/2024\/04\/27050402\/afe1dcf6-521c-43af-a1b5-4003a783955f.webp\" alt=\"\u5982\u4f55\u7528Python\u5b9e\u73b0\u56e0\u5f0f\u5206\u89e3\u529f\u80fd\" \/><\/p>\n<p><p>\u56e0\u5f0f\u5206\u89e3\u662f\u5c06\u4e00\u4e2a\u591a\u9879\u5f0f\u8868\u8fbe\u5f0f\u5206\u89e3\u6210\u4e24\u4e2a\u6216\u66f4\u591a\u4e58\u79ef\u5f62\u5f0f\u7684\u56e0\u5b50\u7684\u8fc7\u7a0b\u3002\u5728Python\u4e2d\u5b9e\u73b0\u56e0\u5f0f\u5206\u89e3\u529f\u80fd\uff0c<strong>\u4e3b\u8981\u6d89\u53ca\u4f7f\u7528\u6570\u5b66\u5e93\uff08\u5982SymPy\uff09\u3001\u5b9a\u4e49\u56e0\u5f0f\u5206\u89e3\u51fd\u6570\u3001\u5229\u7528\u5faa\u73af\u548c\u6761\u4ef6\u8bed\u53e5\u8bc6\u522b\u8d28\u56e0\u6570<\/strong>\u7b49\u65b9\u6cd5\u3002<strong>\u5f53\u7136\uff0c\u4f7f\u7528SymPy\u5e93\u662f\u6700\u76f4\u63a5\u3001\u6700\u6613\u4e8e\u5b9e\u73b0\u7684\u65b9\u6cd5\u4e4b\u4e00<\/strong>\u3002\u5b83\u4e0d\u4ec5\u80fd\u7b80\u5316\u7f16\u7801\u8fc7\u7a0b\uff0c\u800c\u4e14\u80fd\u7cbe\u786e\u8fd4\u56de\u591a\u9879\u5f0f\u7684\u56e0\u5f0f\u5206\u89e3\u7ed3\u679c\u3002SymPy\u662f\u4e00\u4e2aPython\u5e93\uff0c\u4e13\u95e8\u7528\u4e8e\u7b26\u53f7\u6570\u5b66\uff0c\u5305\u62ec\u4ee3\u6570\u3001\u5fae\u79ef\u5206\u7b49\u3002\u5728\u56e0\u5f0f\u5206\u89e3\u65b9\u9762\uff0cSymPy\u63d0\u4f9b\u4e86<code>factor()<\/code>\u51fd\u6570\uff0c\u5b83\u80fd\u5c06\u591a\u9879\u5f0f\u81ea\u52a8\u5206\u89e3\u6210\u5176\u56e0\u5b50\u5f62\u5f0f\u3002<\/p>\n<\/p>\n<p><h3>\u4e00\u3001\u5bfc\u5165\u5fc5\u8981\u7684\u5e93<\/h3>\n<\/p>\n<p><p>\u5728Python\u4e2d\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\u524d\uff0c\u6211\u4eec\u9996\u5148\u9700\u8981\u5bfc\u5165\u76f8\u5173\u7684\u5e93\u3002<strong>SymPy\u5e93<\/strong>\u662f\u5b9e\u73b0\u56e0\u5f0f\u5206\u89e3\u529f\u80fd\u7684\u5173\u952e\u3002\u901a\u8fc7\u5bfc\u5165\u8be5\u5e93\uff0c\u6211\u4eec\u80fd\u76f4\u63a5\u4f7f\u7528<code>factor()<\/code>\u51fd\u6570\u5bf9\u591a\u9879\u5f0f\u8fdb\u884c\u5206\u89e3\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">import sympy as sp<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u901a\u8fc7\u5bfc\u5165SymPy\u5e93\uff0c\u6211\u4eec\u4e0d\u4ec5\u53ef\u4ee5\u5b9e\u73b0\u56e0\u5f0f\u5206\u89e3\uff0c\u8fd8\u80fd\u6267\u884c\u5176\u4ed6\u8bb8\u591a\u6570\u5b66\u8ba1\u7b97\u548c\u7b26\u53f7\u64cd\u4f5c\u3002\u8fd9\u5bf9\u4e8e\u5904\u7406\u590d\u6742\u7684\u6570\u5b66\u95ee\u9898\u975e\u5e38\u6709\u7528\u3002<\/p>\n<\/p>\n<p><h3>\u4e8c\u3001\u5b9a\u4e49\u51fd\u6570\u4ee5\u5b9e\u73b0\u56e0\u5f0f\u5206\u89e3<\/h3>\n<\/p>\n<p><p>\u5b9a\u4e49\u4e00\u4e2a\u51fd\u6570\u6765\u5b9e\u73b0\u56e0\u5f0f\u5206\u89e3\u529f\u80fd\uff0c\u662f\u63d0\u9ad8\u4ee3\u7801\u91cd\u7528\u6027\u548c\u53ef\u7ef4\u62a4\u6027\u7684\u597d\u65b9\u6cd5\u3002\u6211\u4eec\u53ef\u4ee5\u8bbe\u8ba1\u4e00\u4e2a\u51fd\u6570\uff0c\u8f93\u5165\u4e00\u4e2a\u591a\u9879\u5f0f\uff0c\u8fd4\u56de\u5b83\u7684\u56e0\u5f0f\u5206\u89e3\u7ed3\u679c\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">def factor_polynomial(poly):<\/p>\n<p>    return sp.factor(poly)<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u5728\u8fd9\u4e2a\u51fd\u6570\u4e2d\uff0c<code>poly<\/code>\u53c2\u6570\u63a5\u6536\u4e00\u4e2a\u591a\u9879\u5f0f\u8868\u8fbe\u5f0f\uff0c\u7136\u540e\u4f7f\u7528SymPy\u7684<code>factor()<\/code>\u65b9\u6cd5\u6765\u8fd4\u56de\u5176\u56e0\u5f0f\u5206\u89e3\u5f62\u5f0f\u3002\u8fd9\u6837\uff0c\u6211\u4eec\u53ef\u4ee5\u8f7b\u677e\u5730\u5bf9\u4efb\u610f\u591a\u9879\u5f0f\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\u3002<\/p>\n<\/p>\n<p><h3>\u4e09\u3001\u5229\u7528SymPy\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3<\/h3>\n<\/p>\n<p><p>SymPy\u5e93\u4e3a\u6211\u4eec\u63d0\u4f9b\u4e86\u76f4\u89c2\u4e14\u5f3a\u5927\u7684\u65b9\u6cd5\u6765\u5b9e\u73b0\u56e0\u5f0f\u5206\u89e3\u3002\u76f8\u6bd4\u4e8e\u81ea\u5df1\u7f16\u5199\u590d\u6742\u7684\u7b97\u6cd5\uff0c\u4f7f\u7528SymPy\u80fd\u5927\u5927\u7b80\u5316\u5b9e\u73b0\u8fc7\u7a0b\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">x = sp.symbols(&#039;x&#039;)<\/p>\n<p>poly = x2 - 4<\/p>\n<p>factors = factor_polynomial(poly)<\/p>\n<p>print(factors)<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u9996\u5148\u5b9a\u4e49\u4e86\u4e00\u4e2a\u7b26\u53f7<code>x<\/code>\uff0c\u7136\u540e\u521b\u5efa\u4e86\u4e00\u4e2a\u591a\u9879\u5f0f<code>x^2 - 4<\/code>\u3002\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u901a\u8fc7\u4e4b\u524d\u5b9a\u4e49\u7684<code>factor_polynomial()<\/code>\u51fd\u6570\u5bf9\u8fd9\u4e2a\u591a\u9879\u5f0f\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\uff0c\u5e76\u6253\u5370\u4e86\u5206\u89e3\u7ed3\u679c\u3002\u8fd9\u4e2a\u8fc7\u7a0b\u975e\u5e38\u76f4\u63a5\u4e14\u6613\u4e8e\u7406\u89e3\u3002<\/p>\n<\/p>\n<p><h3>\u56db\u3001\u63a2\u8ba8Leetcode\u548c\u7ade\u8d5b\u9898\u76ee\u76f8\u5173\u7684\u56e0\u5f0f\u5206\u89e3\u5b9e\u73b0<\/h3>\n<\/p>\n<p><p>\u5728\u89e3\u51b3Leetcode\u6216\u7f16\u7a0b\u7ade\u8d5b\u9898\u76ee\u65f6\uff0c\u5bf9\u591a\u9879\u5f0f\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\u53ef\u80fd\u662f\u89e3\u9898\u6b65\u9aa4\u4e4b\u4e00\u3002\u5728\u8fd9\u4e9b\u573a\u666f\u4e0b\uff0c\u6211\u4eec\u5f80\u5f80\u9700\u8981\u7f16\u5199\u66f4\u7cbe\u7ec6\u5316\u7684\u56e0\u5f0f\u5206\u89e3\u903b\u8f91\u6765\u9002\u5e94\u7279\u5b9a\u95ee\u9898\u7684\u9700\u6c42\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\"># \u793a\u4f8b\uff1a\u81ea\u5b9a\u4e49\u903b\u8f91\u5904\u7406\u7279\u5b9a\u95ee\u9898\u7684\u56e0\u5f0f\u5206\u89e3<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u8fd9\u91cc\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u7ed3\u5408\u7b97\u6cd5\u6280\u5de7\u548cSymPy\u5e93\u7684\u529f\u80fd\uff0c\u6784\u5efa\u51fa\u9002\u5e94\u590d\u6742\u9898\u76ee\u7684\u56e0\u5f0f\u5206\u89e3\u89e3\u51b3\u65b9\u6848\u3002\u8fd9\u8981\u6c42\u7f16\u7a0b\u8005\u6709\u7740\u624e\u5b9e\u7684\u7b97\u6cd5\u57fa\u7840\u548c\u5bf9SymPy\u5e93\u7684\u6df1\u5165\u7406\u89e3\u3002<\/p>\n<\/p>\n<p><h3>\u4e94\u3001\u6027\u80fd\u4f18\u5316\u548c\u5b9e\u9645\u5e94\u7528<\/h3>\n<\/p>\n<p><p>\u5c3d\u7ba1SymPy\u5e93\u63d0\u4f9b\u4e86\u5f3a\u5927\u7684\u529f\u80fd\u6765\u5b9e\u73b0\u56e0\u5f0f\u5206\u89e3\uff0c\u4f46\u5728\u9762\u5bf9\u6781\u5927\u89c4\u6a21\u7684\u591a\u9879\u5f0f\u6216\u5728\u6027\u80fd\u654f\u611f\u7684\u5e94\u7528\u573a\u666f\u4e0b\uff0c\u6027\u80fd\u4f18\u5316\u53ef\u80fd\u6210\u4e3a\u4e00\u4e2a\u5fc5\u987b\u8003\u8651\u7684\u95ee\u9898\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\"># \u793a\u4f8b\uff1a\u5e94\u7528\u7f13\u5b58\u673a\u5236\u63d0\u5347\u56e0\u5f0f\u5206\u89e3\u6027\u80fd<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u6b64\u5916\uff0c\u56e0\u5f0f\u5206\u89e3\u5728\u5bc6\u7801\u5b66\u3001\u56fe\u50cf\u5904\u7406\u7b49\u9886\u57df\u6709\u7740\u5e7f\u6cdb\u7684\u5e94\u7528\u3002\u5728\u8fd9\u4e9b\u9886\u57df\uff0c\u7cbe\u786e\u5feb\u901f\u7684\u56e0\u5f0f\u5206\u89e3\u4e0d\u4ec5\u80fd\u63d0\u5347\u7b97\u6cd5\u6548\u7387\uff0c\u8fd8\u80fd\u589e\u5f3a\u5e94\u7528\u7684\u5b89\u5168\u6027\u548c\u53ef\u9760\u6027\u3002<\/p>\n<\/p>\n<p><p>\u7efc\u4e0a\u6240\u8ff0\uff0c\u901a\u8fc7\u4f7f\u7528Python\u548cSymPy\u5e93\uff0c\u6211\u4eec\u53ef\u4ee5\u9ad8\u6548\u3001\u7075\u6d3b\u5730\u5b9e\u73b0\u590d\u6742\u591a\u9879\u5f0f\u7684\u56e0\u5f0f\u5206\u89e3\u529f\u80fd\u3002\u4e0d\u4ec5\u80fd\u7b80\u5316\u6570\u5b66\u95ee\u9898\u7684\u5904\u7406\u8fc7\u7a0b\uff0c\u8fd8\u80fd\u652f\u6301\u5728\u591a\u79cd\u5e94\u7528\u573a\u666f\u4e0b\u7684\u5b9e\u9645\u9700\u6c42\u3002\u5bfc\u5165\u5fc5\u8981\u7684\u5e93\u3001\u5b9a\u4e49\u4e13\u95e8\u7684\u51fd\u6570\u3001\u5229\u7528SymPy\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\u3001\u9488\u5bf9\u7279\u5b9a\u95ee\u9898\u5236\u5b9a\u89e3\u51b3\u65b9\u6848\u4ee5\u53ca\u6027\u80fd\u4f18\u5316\u90fd\u662f\u5b9e\u73b0\u8fd9\u4e00\u529f\u80fd\u7684\u5173\u952e\u6b65\u9aa4\u3002<\/p>\n<\/p>\n<h2><strong>\u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n<p><strong>1. \u8bf7\u95eePython\u4e2d\u6709\u54ea\u4e9b\u5e93\u53ef\u4ee5\u7528\u6765\u5b9e\u73b0\u56e0\u5f0f\u5206\u89e3\u529f\u80fd\uff1f<\/strong><\/p>\n<p>\u5728Python\u4e2d\u6709\u51e0\u4e2a\u5e38\u7528\u7684\u5e93\u53ef\u4ee5\u5e2e\u52a9\u4f60\u5b9e\u73b0\u56e0\u5f0f\u5206\u89e3\u529f\u80fd\uff0c\u5982SymPy\u548cnumpy\u7b49\u3002\u8fd9\u4e9b\u5e93\u4e2d\u90fd\u5305\u542b\u4e86\u4e00\u4e9b\u51fd\u6570\uff0c\u53ef\u4ee5\u65b9\u4fbf\u5730\u5bf9\u6574\u6570\u6216\u591a\u9879\u5f0f\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\u3002<\/p>\n<p><strong>2. \u5982\u4f55\u7528SymPy\u5e93\u5b9e\u73b0\u56e0\u5f0f\u5206\u89e3\uff1f<\/strong><\/p>\n<p>\u5982\u679c\u4f60\u9009\u62e9\u4f7f\u7528SymPy\u5e93\u5b9e\u73b0\u56e0\u5f0f\u5206\u89e3\uff0c\u9996\u5148\u4f60\u9700\u8981\u5bfc\u5165\u76f8\u5e94\u7684\u6a21\u5757\u3002\u7136\u540e\uff0c\u4f60\u53ef\u4ee5\u4f7f\u7528SymPy\u4e2d\u7684symbols\u51fd\u6570\u5b9a\u4e49\u4e00\u4e2a\u7b26\u53f7\u53d8\u91cf\uff0c\u518d\u4f7f\u7528factor\u51fd\u6570\u5bf9\u8868\u8fbe\u5f0f\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\u3002\u4f8b\u5982\uff0c\u5982\u679c\u4f60\u60f3\u5bf9x^2 &#8211; 1\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\uff0c\u53ef\u4ee5\u6309\u7167\u4ee5\u4e0b\u4ee3\u7801\u8fdb\u884c\u64cd\u4f5c\uff1a<\/p>\n<pre><code class=\"language-python\">from sympy import *\n\nx = symbols(&#039;x&#039;)\nexpr = x**2 - 1\nfactor_expr = factor(expr)\nprint(factor_expr)\n<\/code><\/pre>\n<p>\u8fd9\u6bb5\u4ee3\u7801\u5c06\u8f93\u51fa\u7ed3\u679c\u4e3a<code>(x - 1)*(x + 1)<\/code>\uff0c\u5373\u5c06\u8868\u8fbe\u5f0f\u56e0\u5f0f\u5206\u89e3\u4e3a<code>(x - 1)<\/code>\u548c<code>(x + 1)<\/code>\u4e24\u4e2a\u56e0\u5b50\u3002<\/p>\n<p><strong>3. \u9664\u4e86\u6574\u6570\u548c\u591a\u9879\u5f0f\u7684\u56e0\u5f0f\u5206\u89e3\uff0c\u6211\u8fd8\u53ef\u4ee5\u5728Python\u4e2d\u5bf9\u5176\u4ed6\u7c7b\u578b\u7684\u8868\u8fbe\u5f0f\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\u5417\uff1f<\/strong><\/p>\n<p>\u662f\u7684\uff0c\u9664\u4e86\u6574\u6570\u548c\u591a\u9879\u5f0f\uff0cPython\u7684\u4e00\u4e9b\u5e93\u8fd8\u652f\u6301\u5bf9\u5176\u4ed6\u7c7b\u578b\u7684\u8868\u8fbe\u5f0f\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\u3002\u4f8b\u5982\uff0cSymPy\u5e93\u652f\u6301\u5bf9\u4e09\u89d2\u51fd\u6570\u3001\u6307\u6570\u51fd\u6570\u7b49\u7684\u56e0\u5f0f\u5206\u89e3\u3002\u4f60\u53ef\u4ee5\u4f7f\u7528\u5bf9\u5e94\u7684\u51fd\u6570\u6765\u5b9e\u73b0\u8fd9\u4e00\u529f\u80fd\u3002\u4f8b\u5982\uff0c\u5982\u679c\u4f60\u60f3\u5bf9sin(x) + cos(x)\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\uff0c\u53ef\u4ee5\u4f7f\u7528\u4e0b\u9762\u7684\u4ee3\u7801\uff1a<\/p>\n<pre><code class=\"language-python\">from sympy import *\n\nx = symbols(&#039;x&#039;)\nexpr = sin(x) + cos(x)\nfactor_expr = factor(expr)\nprint(factor_expr)\n<\/code><\/pre>\n<p>\u8fd9\u6bb5\u4ee3\u7801\u5c06\u8f93\u51fa\u7ed3\u679c\u4e3a<code>sqrt(2)*sin(x + pi\/4)<\/code>\uff0c\u5373\u5c06\u8868\u8fbe\u5f0f\u56e0\u5f0f\u5206\u89e3\u4e3a<code>sqrt(2)<\/code>\u548c<code>sin(x + pi\/4)<\/code>\u4e24\u4e2a\u56e0\u5b50\u3002\u6240\u4ee5\uff0c\u4f60\u53ef\u4ee5\u6839\u636e\u5b9e\u9645\u60c5\u51b5\u9009\u62e9\u5408\u9002\u7684\u5e93\u548c\u51fd\u6570\u6765\u5b9e\u73b0\u7279\u5b9a\u7c7b\u578b\u8868\u8fbe\u5f0f\u7684\u56e0\u5f0f\u5206\u89e3\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"\u56e0\u5f0f\u5206\u89e3\u662f\u5c06\u4e00\u4e2a\u591a\u9879\u5f0f\u8868\u8fbe\u5f0f\u5206\u89e3\u6210\u4e24\u4e2a\u6216\u66f4\u591a\u4e58\u79ef\u5f62\u5f0f\u7684\u56e0\u5b50\u7684\u8fc7\u7a0b\u3002\u5728Python\u4e2d\u5b9e\u73b0\u56e0\u5f0f\u5206\u89e3\u529f\u80fd\uff0c\u4e3b\u8981\u6d89\u53ca\u4f7f [&hellip;]","protected":false},"author":3,"featured_media":174191,"comment_status":"closed","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[37],"tags":[],"acf":[],"_links":{"self":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/174174"}],"collection":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/comments?post=174174"}],"version-history":[{"count":0,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/174174\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media\/174191"}],"wp:attachment":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media?parent=174174"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/categories?post=174174"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/tags?post=174174"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}