{"id":1100265,"date":"2025-01-08T15:38:21","date_gmt":"2025-01-08T07:38:21","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/1100265.html"},"modified":"2025-01-08T15:38:24","modified_gmt":"2025-01-08T07:38:24","slug":"%e5%a6%82%e4%bd%95%e7%94%a8python%e7%bc%96%e7%a8%8b%e8%a7%a3%e6%9c%aa%e7%9f%a5%e6%95%b0-2","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/1100265.html","title":{"rendered":"\u5982\u4f55\u7528python\u7f16\u7a0b\u89e3\u672a\u77e5\u6570"},"content":{"rendered":"

\"\u5982\u4f55\u7528python\u7f16\u7a0b\u89e3\u672a\u77e5\u6570\"<\/p>\n

\u4f7f\u7528Python\u7f16\u7a0b\u89e3\u672a\u77e5\u6570\u7684\u65b9\u6cd5\u6709\uff1a\u4f7f\u7528SymPy\u5e93\u3001NumPy\u5e93\u3001SciPy\u5e93\u3001\u624b\u52a8\u5b9e\u73b0\u65b9\u7a0b\u6c42\u89e3\u3002\u5176\u4e2d\uff0c\u4f7f\u7528SymPy\u5e93\u662f\u6700\u5e38\u89c1\u4e14\u65b9\u4fbf\u7684\u65b9\u6cd5\u3002\u4e0b\u9762\u8be6\u7ec6\u4ecb\u7ecdSymPy\u5e93\u7684\u4f7f\u7528\u3002<\/strong><\/p>\n<\/p>\n

SymPy\u5e93<\/strong>\u662fPython\u7684\u4e00\u4e2a\u7b26\u53f7\u6570\u5b66\u5e93\uff0c\u5b83\u53ef\u4ee5\u7528\u6765\u8fdb\u884c\u7b26\u53f7\u8ba1\u7b97\uff0c\u6bd4\u5982\u6c42\u89e3\u65b9\u7a0b\u3001\u6781\u9650\u3001\u79ef\u5206\u3001\u5bfc\u6570\u7b49\u3002\u4f7f\u7528SymPy\u5e93\u89e3\u672a\u77e5\u6570\u7684\u6b65\u9aa4\u4e3b\u8981\u5305\u62ec\u5b9a\u4e49\u7b26\u53f7\u53d8\u91cf\u3001\u6784\u9020\u65b9\u7a0b\u3001\u8c03\u7528\u89e3\u65b9\u7a0b\u7684\u51fd\u6570\u3002\u4e0b\u9762\u6211\u4eec\u8be6\u7ec6\u4ecb\u7ecd\u5982\u4f55\u4f7f\u7528SymPy\u5e93\u89e3\u672a\u77e5\u6570\u3002<\/p>\n<\/p>\n

\u4e00\u3001\u5b89\u88c5\u4e0e\u5bfc\u5165SymPy\u5e93<\/h3>\n<\/p>\n

\u5728\u4f7f\u7528SymPy\u5e93\u4e4b\u524d\uff0c\u4f60\u9700\u8981\u786e\u4fdd\u5df2\u7ecf\u5b89\u88c5\u4e86SymPy\u5e93\u3002\u5982\u679c\u4f60\u8fd8\u6ca1\u6709\u5b89\u88c5\uff0c\u53ef\u4ee5\u4f7f\u7528\u4ee5\u4e0b\u547d\u4ee4\u6765\u5b89\u88c5\uff1a<\/p>\n<\/p>\n

pip install sympy<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u5b89\u88c5\u5b8c\u6210\u540e\uff0c\u53ef\u4ee5\u5728Python\u811a\u672c\u4e2d\u5bfc\u5165SymPy\u5e93\uff1a<\/p>\n<\/p>\n
import sympy as sp<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u4e8c\u3001\u5b9a\u4e49\u7b26\u53f7\u53d8\u91cf<\/h3>\n<\/p>\n
\u5728\u4f7f\u7528SymPy\u5e93\u8fdb\u884c\u7b26\u53f7\u8ba1\u7b97\u4e4b\u524d\uff0c\u9700\u8981\u5148\u5b9a\u4e49\u7b26\u53f7\u53d8\u91cf\u3002SymPy\u63d0\u4f9b\u4e86symbols<\/code>\u51fd\u6570\u6765\u5b9a\u4e49\u7b26\u53f7\u53d8\u91cf\u3002\u4f8b\u5982\uff0c\u5b9a\u4e49\u4e00\u4e2a\u7b26\u53f7\u53d8\u91cfx\uff1a<\/p>\n<\/p>\n
x = sp.symbols('x')<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u4f60\u4e5f\u53ef\u4ee5\u4e00\u6b21\u6027\u5b9a\u4e49\u591a\u4e2a\u7b26\u53f7\u53d8\u91cf\uff1a<\/p>\n<\/p>\n
x, y, z = sp.symbols('x y z')<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u4e09\u3001\u6784\u9020\u65b9\u7a0b<\/h3>\n<\/p>\n
\u5728\u5b9a\u4e49\u4e86\u7b26\u53f7\u53d8\u91cf\u4e4b\u540e\uff0c\u53ef\u4ee5\u4f7f\u7528\u8fd9\u4e9b\u7b26\u53f7\u53d8\u91cf\u6784\u9020\u65b9\u7a0b\u3002\u4f8b\u5982\uff0c\u6784\u9020\u4e00\u4e2a\u7b80\u5355\u7684\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b\uff1a<\/p>\n<\/p>\n
equation = sp.Eq(2 * x + 3, 7)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u8fd9\u91ccsp.Eq<\/code>\u51fd\u6570\u7528\u4e8e\u6784\u9020\u7b49\u5f0f\uff0c\u7b49\u53f7\u5de6\u8fb9\u4e3a\u65b9\u7a0b\u7684\u5de6\u8fb9\uff0c\u7b49\u53f7\u53f3\u8fb9\u4e3a\u65b9\u7a0b\u7684\u53f3\u8fb9\u3002<\/p>\n<\/p>\n
\u56db\u3001\u6c42\u89e3\u65b9\u7a0b<\/h3>\n<\/p>\n
\u4f7f\u7528SymPy\u5e93\u63d0\u4f9b\u7684solve<\/code>\u51fd\u6570\u53ef\u4ee5\u6c42\u89e3\u65b9\u7a0b\u3002solve<\/code>\u51fd\u6570\u7684\u7b2c\u4e00\u4e2a\u53c2\u6570\u662f\u65b9\u7a0b\uff0c\u7b2c\u4e8c\u4e2a\u53c2\u6570\u662f\u9700\u8981\u6c42\u89e3\u7684\u53d8\u91cf\u3002\u4f8b\u5982\uff0c\u6c42\u89e3\u4e0a\u9762\u7684\u65b9\u7a0b\uff1a<\/p>\n<\/p>\n
solution = sp.solve(equation, x)<\/p>\n
print(solution)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u8fd0\u884c\u8fd9\u6bb5\u4ee3\u7801\uff0c\u4f1a\u8f93\u51fa\u65b9\u7a0b\u7684\u89e3\u3002<\/p>\n<\/p>\n
\u4e94\u3001\u89e3\u591a\u5143\u65b9\u7a0b\u7ec4<\/h3>\n<\/p>\n
SymPy\u5e93\u4e0d\u4ec5\u53ef\u4ee5\u6c42\u89e3\u4e00\u5143\u65b9\u7a0b\uff0c\u8fd8\u53ef\u4ee5\u6c42\u89e3\u591a\u5143\u65b9\u7a0b\u7ec4\u3002\u5047\u8bbe\u6211\u4eec\u6709\u4ee5\u4e0b\u4e24\u4e2a\u65b9\u7a0b\uff1a<\/p>\n<\/p>\n
2x + y = 3<\/p>\n
x - y = 1<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u53ef\u4ee5\u8fd9\u6837\u6784\u9020\u65b9\u7a0b\u7ec4\u5e76\u6c42\u89e3\uff1a<\/p>\n<\/p>\n
# \u5b9a\u4e49\u7b26\u53f7\u53d8\u91cf<\/p>\n
x, y = sp.symbols('x y')<\/p>\n
\u6784\u9020\u65b9\u7a0b<\/strong><\/h2>\n
equation1 = sp.Eq(2 * x + y, 3)<\/p>\n
equation2 = sp.Eq(x - y, 1)<\/p>\n
\u6c42\u89e3\u65b9\u7a0b\u7ec4<\/strong><\/h2>\n
solution = sp.solve((equation1, equation2), (x, y))<\/p>\n
print(solution)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u8fd0\u884c\u8fd9\u6bb5\u4ee3\u7801\uff0c\u4f1a\u8f93\u51fa\u65b9\u7a0b\u7ec4\u7684\u89e3\u3002<\/p>\n<\/p>\n
\u516d\u3001\u89e3\u975e\u7ebf\u6027\u65b9\u7a0b<\/h3>\n<\/p>\n
SymPy\u5e93\u8fd8\u53ef\u4ee5\u6c42\u89e3\u975e\u7ebf\u6027\u65b9\u7a0b\u3002\u4f8b\u5982\uff0c\u6c42\u89e3\u4ee5\u4e0b\u975e\u7ebf\u6027\u65b9\u7a0b\uff1a<\/p>\n<\/p>\n
x^2 - 4x + 4 = 0<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u53ef\u4ee5\u8fd9\u6837\u6784\u9020\u65b9\u7a0b\u5e76\u6c42\u89e3\uff1a<\/p>\n<\/p>\n
# \u5b9a\u4e49\u7b26\u53f7\u53d8\u91cf<\/p>\n
x = sp.symbols('x')<\/p>\n
\u6784\u9020\u65b9\u7a0b<\/strong><\/h2>\n
equation = sp.Eq(x2 - 4*x + 4, 0)<\/p>\n
\u6c42\u89e3\u65b9\u7a0b<\/strong><\/h2>\n
solution = sp.solve(equation, x)<\/p>\n
print(solution)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u8fd0\u884c\u8fd9\u6bb5\u4ee3\u7801\uff0c\u4f1a\u8f93\u51fa\u65b9\u7a0b\u7684\u89e3\u3002<\/p>\n<\/p>\n
\u4e03\u3001\u4f7f\u7528NumPy\u5e93\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4<\/h3>\n<\/p>\n
\u9664\u4e86SymPy\u5e93\uff0cNumPy\u5e93\u4e5f\u53ef\u4ee5\u7528\u6765\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4\u3002NumPy\u5e93\u4e3b\u8981\u7528\u4e8e\u6570\u503c\u8ba1\u7b97\uff0c\u9002\u5408\u5904\u7406\u5927\u89c4\u6a21\u6570\u636e\u548c\u77e9\u9635\u8fd0\u7b97\u3002\u4e0b\u9762\u662f\u4f7f\u7528NumPy\u5e93\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4\u7684\u793a\u4f8b\uff1a<\/p>\n<\/p>\n
import numpy as np<\/p>\n
\u7cfb\u6570\u77e9\u9635<\/strong><\/h2>\n
A = np.array([[2, 1], [1, -1]])<\/p>\n
\u5e38\u6570\u9879<\/strong><\/h2>\n
B = np.array([3, 1])<\/p>\n
\u6c42\u89e3\u65b9\u7a0b\u7ec4<\/strong><\/h2>\n
solution = np.linalg.solve(A, B)<\/p>\n
print(solution)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u516b\u3001\u4f7f\u7528SciPy\u5e93\u89e3\u975e\u7ebf\u6027\u65b9\u7a0b<\/h3>\n<\/p>\n
SciPy\u5e93\u662f\u4e00\u4e2a\u7528\u4e8e\u79d1\u5b66\u8ba1\u7b97\u7684\u5e93\uff0c\u53ef\u4ee5\u7528\u6765\u89e3\u975e\u7ebf\u6027\u65b9\u7a0b\u3002\u4e0b\u9762\u662f\u4f7f\u7528SciPy\u5e93\u89e3\u975e\u7ebf\u6027\u65b9\u7a0b\u7684\u793a\u4f8b\uff1a<\/p>\n<\/p>\n
from scipy.optimize import fsolve<\/p>\n
\u5b9a\u4e49\u975e\u7ebf\u6027\u65b9\u7a0b<\/strong><\/h2>\n
def equation(x):<\/p>\n
    return x2 - 4*x + 4<\/p>\n
\u6c42\u89e3\u65b9\u7a0b<\/strong><\/h2>\n
solution = fsolve(equation, 0)<\/p>\n
print(solution)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u4e5d\u3001\u603b\u7ed3<\/h3>\n<\/p>\n
\u672c\u6587\u4ecb\u7ecd\u4e86\u5982\u4f55\u4f7f\u7528Python\u7f16\u7a0b\u89e3\u672a\u77e5\u6570\u7684\u65b9\u6cd5\uff0c\u4e3b\u8981\u5305\u62ec\u4f7f\u7528SymPy\u5e93\u3001NumPy\u5e93\u3001SciPy\u5e93\u4ee5\u53ca\u624b\u52a8\u5b9e\u73b0\u65b9\u7a0b\u6c42\u89e3\u3002SymPy\u5e93\u662f\u6700\u5e38\u89c1\u4e14\u65b9\u4fbf\u7684\u65b9\u6cd5<\/strong>\uff0c\u53ef\u4ee5\u7528\u6765\u6c42\u89e3\u4e00\u5143\u65b9\u7a0b\u3001\u591a\u5143\u65b9\u7a0b\u7ec4\u4ee5\u53ca\u975e\u7ebf\u6027\u65b9\u7a0b\u3002NumPy\u5e93\u9002\u5408\u5904\u7406\u5927\u89c4\u6a21\u6570\u636e\u548c\u77e9\u9635\u8fd0\u7b97<\/strong>\uff0c\u53ef\u4ee5\u7528\u6765\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4\u3002SciPy\u5e93\u5219\u7528\u4e8e\u79d1\u5b66\u8ba1\u7b97<\/strong>\uff0c\u53ef\u4ee5\u7528\u6765\u89e3\u975e\u7ebf\u6027\u65b9\u7a0b\u3002\u5e0c\u671b\u901a\u8fc7\u672c\u6587\u7684\u4ecb\u7ecd\uff0c\u80fd\u591f\u5e2e\u52a9\u4f60\u66f4\u597d\u5730\u4f7f\u7528Python\u7f16\u7a0b\u89e3\u672a\u77e5\u6570\u3002<\/p>\n<\/p>\n
\u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n
 \u5982\u4f55\u7528Python\u7f16\u7a0b\u6c42\u89e3\u65b9\u7a0b\u4e2d\u7684\u672a\u77e5\u6570\uff1f<\/strong>
\u5728Python\u4e2d\uff0c\u53ef\u4ee5\u4f7f\u7528\u591a\u79cd\u5e93\u6765\u6c42\u89e3\u5305\u542b\u672a\u77e5\u6570\u7684\u65b9\u7a0b\u3002\u6700\u5e38\u7528\u7684\u5e93\u662fSymPy\uff0c\u5b83\u662f\u4e00\u4e2a\u5f3a\u5927\u7684\u7b26\u53f7\u6570\u5b66\u5e93\u3002\u901a\u8fc7\u5b9a\u4e49\u65b9\u7a0b\u5e76\u8c03\u7528\u6c42\u89e3\u51fd\u6570\uff0c\u4f60\u53ef\u4ee5\u8f7b\u677e\u627e\u5230\u672a\u77e5\u6570\u7684\u503c\u3002\u6b64\u5916\uff0cNumPy\u5e93\u4e5f\u53ef\u4ee5\u7528\u4e8e\u6570\u503c\u6c42\u89e3\uff0c\u7279\u522b\u662f\u5bf9\u4e8e\u7ebf\u6027\u65b9\u7a0b\u7ec4\u3002<\/p>\n
Python\u89e3\u65b9\u7a0b\u65f6\u9700\u8981\u6ce8\u610f\u54ea\u4e9b\u5e38\u89c1\u95ee\u9898\uff1f<\/strong>
\u5728\u4f7f\u7528Python\u89e3\u65b9\u7a0b\u65f6\uff0c\u4e00\u4e9b\u5e38\u89c1\u7684\u95ee\u9898\u5305\u62ec\u65b9\u7a0b\u7684\u5f62\u5f0f\u3001\u53d8\u91cf\u7684\u5b9a\u4e49\u4ee5\u53ca\u89e3\u7684\u5b58\u5728\u6027\u3002\u5982\u679c\u65b9\u7a0b\u7684\u5f62\u5f0f\u4e0d\u6807\u51c6\uff0c\u53ef\u80fd\u4f1a\u5bfc\u81f4\u6c42\u89e3\u5931\u8d25\u3002\u786e\u4fdd\u4f60\u5b9a\u4e49\u7684\u65b9\u7a0b\u662f\u6b63\u786e\u7684\uff0c\u5e76\u4e14\u4e86\u89e3\u662f\u5426\u5b58\u5728\u89e3\u662f\u975e\u5e38\u91cd\u8981\u7684\u3002<\/p>\n
\u6709\u54ea\u4e9bPython\u5e93\u53ef\u4ee5\u5e2e\u52a9\u6211\u89e3\u51b3\u4e0d\u540c\u7c7b\u578b\u7684\u65b9\u7a0b\uff1f<\/strong>
\u9664\u4e86SymPy\uff0c\u8fd8\u6709\u5176\u4ed6\u4e00\u4e9bPython\u5e93\u53ef\u4ee5\u7528\u6765\u6c42\u89e3\u65b9\u7a0b\u3002SciPy\u662f\u4e00\u4e2a\u7528\u4e8e\u79d1\u5b66\u8ba1\u7b97\u7684\u5e93\uff0c\u63d0\u4f9b\u4e86\u591a\u79cd\u6c42\u89e3\u5668\uff0c\u9002\u7528\u4e8e\u6570\u503c\u89e3\u3002\u6b64\u5916\uff0cNumPy\u7528\u4e8e\u5904\u7406\u6570\u7ec4\u548c\u77e9\u9635\u8fd0\u7b97\uff0c\u9002\u5408\u7ebf\u6027\u65b9\u7a0b\u7ec4\u7684\u6c42\u89e3\u3002\u5982\u679c\u4f60\u9700\u8981\u5904\u7406\u975e\u7ebf\u6027\u65b9\u7a0b\uff0cSciPy\u7684optimize\u6a21\u5757\u4e5f\u63d0\u4f9b\u4e86\u76f8\u5173\u7684\u51fd\u6570\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"\u4f7f\u7528Python\u7f16\u7a0b\u89e3\u672a\u77e5\u6570\u7684\u65b9\u6cd5\u6709\uff1a\u4f7f\u7528SymPy\u5e93\u3001NumPy\u5e93\u3001SciPy\u5e93\u3001\u624b\u52a8\u5b9e\u73b0\u65b9\u7a0b\u6c42\u89e3\u3002\u5176\u4e2d\uff0c\u4f7f […]","protected":false},"author":3,"featured_media":1100276,"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\/1100265"}],"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=1100265"}],"version-history":[{"count":"1","href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/1100265\/revisions"}],"predecessor-version":[{"id":1100278,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/1100265\/revisions\/1100278"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media\/1100276"}],"wp:attachment":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media?parent=1100265"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/categories?post=1100265"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/tags?post=1100265"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}