± 笛卡尔符号法则计算器Descartes' Rule of Signs Calculator
输入多项式（如 x^3 - 3x^2 + 4）或系数列表，用笛卡尔符号法则统计 P(x) 和 P(−x) 的变号次数，列出正实根、负实根和虚根个数的所有可能组合。Enter a polynomial (e.g. x^3 - 3x^2 + 4) or its coefficients to count sign changes in P(x) and P(−x) with Descartes' rule of signs and list every possible mix of positive, negative and complex roots.
使用说明与常见问题How-to & FAQ
「笛卡尔符号法则计算器」是什么？What is the Descartes' Rule of Signs Calculator tool?
输入多项式（如 x^3 - 3x^2 + 4）或系数列表，用笛卡尔符号法则统计 P(x) 和 P(−x) 的变号次数，列出正实根、负实根和虚根个数的所有可能组合。Enter a polynomial (e.g. x^3 - 3x^2 + 4) or its coefficients to count sign changes in P(x) and P(−x) with Descartes' rule of signs and list every possible mix of positive, negative and complex roots.
如何使用「笛卡尔符号法则计算器」？How do I use the Descartes' Rule of Signs Calculator tool?
在「笛卡尔符号法则计算器」中，填写「多项式或系数（从最高次起，如 1 -3 0 4）」等参数，结果会随输入实时计算并显示在下方。In the Descartes' Rule of Signs Calculator: Fill in "Polynomial or coefficients (highest power first, e.g. 1 -3 0 4)"; results are recalculated instantly as you type.
笛卡尔符号法则是什么？What is Descartes' rule of signs?
按降幂排列多项式系数（跳过 0），相邻系数符号改变的次数为 V，则正实根的个数等于 V 或比 V 少一个偶数。把 x 换成 −x 再数一次，得到负实根的可能个数。Write the coefficients in descending order (skipping zeros) and count sign changes V: the number of positive real roots is V or less than V by an even number. Replace x with −x and count again for negative roots.
虚根个数怎么得到？How is the complex-root count found?
总根数等于次数。用次数减去正、负实根和零根的个数，剩下的是虚根；虚根成对出现，所以只保留偶数的组合。There are as many roots as the degree. Subtract the positive, negative and zero roots; the rest are complex, which come in pairs, so only even counts are kept.
计算精度如何？How precise are the results?
「笛卡尔符号法则计算器」使用 JavaScript 双精度浮点数（约 15–16 位有效数字）；极大或极小的数值可能存在精度误差。The Descartes' Rule of Signs Calculator uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.
「笛卡尔符号法则计算器」免费吗？需要注册吗？Is the Descartes' Rule of Signs Calculator free? Do I need an account?
「笛卡尔符号法则计算器」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Descartes' Rule of Signs Calculator is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.