± 生成 Rudin–Shapiro 序列Generate Rudin–Shapiro Sequence

使用说明与常见问题How-to & FAQ

「生成 Rudin–Shapiro 序列」是什么？What is the Generate Rudin–Shapiro Sequence tool?

生成 Rudin–Shapiro 序列：±1 值，与二进制中相邻 11 的个数奇偶相关。本地处理。可设置「项数」、「每行一个」。Generate the Rudin–Shapiro sequence of ±1 from the parity of adjacent 11-bits in n. Processed locally. Settings: Terms, One per line.

如何使用「生成 Rudin–Shapiro 序列」？How do I use the Generate Rudin–Shapiro Sequence tool?

在「生成 Rudin–Shapiro 序列」中，按需设置「项数」，结果会实时显示在下方，点击「复制结果」即可复制。In the Generate Rudin–Shapiro Sequence: Adjust "Terms"; the result appears below instantly — click "Copy result" to copy it.

Rudin–Shapiro 序列有什么用？What is the Rudin–Shapiro sequence used for?

第 n 项是 +1 还是 −1，取决于 n 的二进制中相邻「11」出现次数的奇偶。它最初用来构造系数为 ±1、最大值只有约 √N 量级的三角多项式，也是自动序列的经典例子。Term n is +1 or −1 depending on whether the binary form of n contains an even or odd number of adjacent 11 pairs. It was introduced to build ±1 trigonometric polynomials whose maximum is only of order √N, and is a classic automatic sequence.

输入和输出是什么样的？What does the input and output look like?

例如在「生成 Rudin–Shapiro 序列」中把「项数」设为 8，输出为：+1 +1 +1 -1 +1 +1 -1 +1。For example, in the Generate Rudin–Shapiro Sequence with "Terms" set to 8, the output is: +1 +1 +1 -1 +1 +1 -1 +1.

有哪些选项可以调整？What options can I adjust?

「生成 Rudin–Shapiro 序列」的设置：「项数」默认 32；可勾选：「每行一个」。每次生成结果都按当前设置处理。Settings in the Generate Rudin–Shapiro Sequence — "Terms" default 32; tick boxes: "One per line". The result always uses the current settings.

计算精度如何？How precise are the results?

「生成 Rudin–Shapiro 序列」输出的每一项都是精确的整数（只有 +1 和 −1，按二进制中 11 的个数得到），计算中没有舍入，也不涉及浮点精度问题。Every term the Generate Rudin–Shapiro Sequence outputs is an exact integer (only +1 and −1, from counting 11 pairs in binary); there is no rounding and floating-point precision never comes into play.

「生成 Rudin–Shapiro 序列」免费吗？需要注册吗？Is the Generate Rudin–Shapiro Sequence free? Do I need an account?

「生成 Rudin–Shapiro 序列」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 Generate Rudin–Shapiro Sequence is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.