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Warning: Cannot modify header information - headers already sent by (output started at /data/wiki/inc/init.php:239) in /data/wiki/inc/httputils.php on line 29 CVBB ACM Team 2020-2021:teams:hotpot:aspirine
https://wiki.cvbbacm.com/
2025-07-02T20:28:14+0800CVBB ACM Team
https://wiki.cvbbacm.com/
https://wiki.cvbbacm.com/lib/exe/fetch.php?media=favicon.icotext/html2020-05-08T18:03:39+0800Anonymous (anonymous@undisclosed.example.com)2020-2021:teams:hotpot:aspirine:多项式对数函数
https://wiki.cvbbacm.com/doku.php?id=2020-2021:teams:hotpot:aspirine:%E5%A4%9A%E9%A1%B9%E5%BC%8F%E5%AF%B9%E6%95%B0%E5%87%BD%E6%95%B0&rev=1588932219&do=diff
问题描述
给定一个n-1次多项式$f(x)$，保证$a_0=1$。求$\ln(f(x))$对$x^n$取模的结果。系数模998244353
$\ln(f(x))$定义为其幂级数展开，对$x^n$取模为其幂级数的前n项和。
解决方法
前置知识
多项式乘法（NTT），多项式求逆，多项式求导、积分（这个所有人都会）$g(x)=\ln(f(x))$$g'(x)\equiv\frac{f'(x)}{f(x)}\equiv f'(x)f^{-1}(x)\pmod{x^n}$$f^{-1}(x)$$x^n$$f'(x)$$f'(x)f^{-1}(x)$$g'(x)$$x^n$$g(x)$text/html2020-07-17T15:48:10+0800Anonymous (anonymous@undisclosed.example.com)2020-2021:teams:hotpot:aspirine:矩阵树定理
https://wiki.cvbbacm.com/doku.php?id=2020-2021:teams:hotpot:aspirine:%E7%9F%A9%E9%98%B5%E6%A0%91%E5%AE%9A%E7%90%86&rev=1594972090&do=diff
问题描述