Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

refactor(linear-recurrence.md): 重写然后加了 Bostan--Mori 算法 #5615

Open
wants to merge 4 commits into
base: master
Choose a base branch
from

Conversation

hly1204
Copy link
Contributor

@hly1204 hly1204 commented May 19, 2024

  • 我已认真阅读贡献指南 (contributing guidelines) 和社区公约 (code of conduct),并遵循了如何参与页及格式手册页的相应规范。

@HeRaNO
Copy link
Collaborator

HeRaNO commented May 20, 2024

https://oi-wiki.org/math/number-theory/quad-residue/#bostanmori-%E7%AE%97%E6%B3%95 这里也有 Bostan-Mori 算法,这两个位置是否应该只保留一个,还是另做修改?

OI Wiki 是一个编程竞赛知识整合站点,提供有趣又实用的编程竞赛知识以及其他有帮助的内容,帮助广大编程竞赛爱好者更快更深入地学习编程竞赛

@hly1204
Copy link
Contributor Author

hly1204 commented May 20, 2024

https://oi-wiki.org/math/number-theory/quad-residue/#bostanmori-%E7%AE%97%E6%B3%95 这里也有 Bostan-Mori 算法,这两个位置是否应该只保留一个,还是另做修改?

我觉得可以不用修改,因为这个是一个特例,类似于斐波那契数列那种。而且其实还得说明一下 $x^k \bmod{F(x)}$$\dfrac{1}{x^{\deg{F}}F(x^{-1})}$ 的一部分是一样的(虽然比较显然吧),这里还没有说明,可能以后补一下。

OI Wiki 是一个编程竞赛知识整合站点,提供有趣又实用的编程竞赛知识以及其他有帮助的内容,帮助广大编程竞赛爱好者更快更深入地学习编程竞赛


$$
v_t=\begin{bmatrix}f_t\\f_{t+1}\\\vdots\\f_{t+k-1}\end{bmatrix}
\begin{aligned}
\left\langle \left(\sum_{j=1}^{d-1}c_{d-j+1}x^j\right)+c_1\left(\sum_{j=1}^dc_{d-j+1}x^{j-1}\right),A(x)\right\rangle &=\left\langle \sum_{j=1}^{d-1}c_{d-j+1}x^j,A(x)\right\rangle+c_1\left\langle \sum_{j=1}^dc_{d-j+1}x^{j-1},A(x)\right\rangle \\
Copy link
Member

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

这一行太长了

那么对于 $V(x^2)=Q(x)Q(-x)$ 而言,我们只需求出

$$
\left\lbrack x^{\left\lbrack \left\lceil \frac{L-\deg Q}{2}\right\rceil,\left\lceil \frac{L+\deg Q+1}{2}\right\rceil\right)}\right\rbrack \frac{1}{V(x)}
Copy link
Member

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

Suggested change
\left\lbrack x^{\left\lbrack \left\lceil \frac{L-\deg Q}{2}\right\rceil,\left\lceil \frac{L+\deg Q+1}{2}\right\rceil\right)}\right\rbrack \frac{1}{V(x)}
\left\lbrack x^{\left\lbrack \lceil (L-\deg Q)/2 \rceil,\lceil (L+\deg Q+1)/2 \rceil\right)}\right\rbrack \frac{1}{V(x)}

上标字号太小了

Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment
Projects
None yet
Development

Successfully merging this pull request may close these issues.

None yet

4 participants