Conversation
![llamapreview[bot]](https://avatars.githubusercontent.com/in/1023541?s=60&v=4){kind=small}
There was a problem hiding this comment.
Auto Pull Request Review from LlamaPReview
Large PR Notification
Dear contributor,
Thank you for your substantial contribution to this project. LlamaPReview has detected that this Pull Request contains a large volume of changes, which exceeds our current processing capacity.
Details:
- PR and related contents total size: Approximately 332,425 characters
- Current limit: 256,000 characters
Next steps:
- Consider breaking this PR into smaller, more focused changes if possible.
- For manual review, please reach out to your team members or maintainers.
We appreciate your understanding and commitment to improving this project. Your contributions are valuable, and we want to ensure they receive the attention they deserve.
LlamaPReview is continuously evolving to better serve the community. Share your thoughts on handling large PRs in our GitHub Discussions - your feedback helps us improve and expand our capabilities.
If you have any questions or need assistance, our community and support team are here to help.
Best regards,
LlamaPReview Team
![cubic-dev-ai[bot]](https://avatars.githubusercontent.com/in/1082092?s=60&v=4){kind=small}
There was a problem hiding this comment.
40 issues found across 28 files
Confidence score: 3/5
- Multiple high-severity math errors in
docs/science/function/7.mdanddocs/science/polynomial/1.mdrisk publishing incorrect formulas and derivations. Taskfile.ymluses the wrongSITE_URLhost (github.comvsgithub.io), which can produce broken absolute URLs intask buildoutput.- Given the number of concrete correctness issues, this is a moderate-risk merge despite being doc-focused.
- Pay close attention to
docs/science/function/7.md,docs/science/polynomial/1.md,docs/science/polynomial/2.md,Taskfile.yml- incorrect formulas and build URL settings.
Prompt for AI agents (unresolved issues)
Check if these issues are valid — if so, understand the root cause of each and fix them. If appropriate, use sub-agents to investigate and fix each issue separately.
<file name="docs/science/polynomial/2.md">
<violation number="1" location="docs/science/polynomial/2.md:165">
P2: This derivation line mixes `q` and `a`, so it does not actually derive the characteristic equation from `a_n=q^n`.</violation>
<violation number="2" location="docs/science/polynomial/2.md:199">
P1: The recurrence is misstated here: `y_{n-2}` should be `y a_{n-2}`.</violation>
<violation number="3" location="docs/science/polynomial/2.md:433">
P2: This rearrangement has the wrong sign: `x^2-x=3x-4` simplifies to `x^2-4x+4=0`, not `x^2-4x-4=0`.</violation>
<violation number="4" location="docs/science/polynomial/2.md:616">
P2: The triple-angle formula for sine is wrong here: the last term should be `4\sin^3\theta`, not `4\sin^2\theta`.</violation>
<violation number="5" location="docs/science/polynomial/2.md:620">
P2: The triple-angle formula for cosine is wrong here: the first term should be `4\cos^3\theta`, not `4\cos^2\theta`.</violation>
</file>
<file name="docs/science/function/7.md">
<violation number="1" location="docs/science/function/7.md:82">
P1: `\cos x` is not an infinitesimal at `x \to 0`, so this equivalence chain is false.</violation>
<violation number="2" location="docs/science/function/7.md:176">
P1: The quotient-rule formula is missing the `g^2(x)` denominator, so the identity is false.</violation>
<violation number="3" location="docs/science/function/7.md:211">
P1: The evaluated `\int_a^b n^x\,dx` formula uses `\ln a`/`\ln b` in the denominator, which is incorrect.</violation>
<violation number="4" location="docs/science/function/7.md:255">
P1: This back-substitution drops the square on `(x^2+1)`, so the antiderivative is wrong.</violation>
<violation number="5" location="docs/science/function/7.md:292">
P2: The stated domain for the Gamma recurrence is reversed: `\Gamma` is undefined at non-positive integers.</violation>
<violation number="6" location="docs/science/function/7.md:377">
P2: This inequality should be `1/a_{100} < 40`, not `1/40`; the current line invalidates the bound.</violation>
</file>
<file name="docs/science/polynomial/1.md">
<violation number="1" location="docs/science/polynomial/1.md:365">
P2: This general term labels the wrong symbol as the common difference: for `a_n=d+qn`, the difference is `q`, not `d`.</violation>
<violation number="2" location="docs/science/polynomial/1.md:560">
P1: The boxed sum formula is incorrect: the `d` should be attached to `(n-1)`, not multiplied across the entire bracket.</violation>
<violation number="3" location="docs/science/polynomial/1.md:680">
P2: The accumulated sum repeats `f(2)`; it should continue with `f(3)` through `f(n)`.</violation>
<violation number="4" location="docs/science/polynomial/1.md:782">
P2: Adding a constant to a geometric sequence does not generally produce another geometric sequence.</violation>
<violation number="5" location="docs/science/polynomial/1.md:889">
P1: This partial-fraction identity is wrong; the first term should be `1/n`, not `1/k`.</violation>
<violation number="6" location="docs/science/polynomial/1.md:920">
P2: The telescoped remainder should end with `-1/(n+2)`, not `-1/(n-2)`.</violation>
<violation number="7" location="docs/science/polynomial/1.md:1284">
P2: These recurrence expansions use the wrong indices, so the telescoping derivation is invalid.</violation>
</file>
<file name="Taskfile.yml">
<violation number="1" location="Taskfile.yml:6">
P1: `SITE_URL` uses `github.com` instead of the GitHub Pages host `github.io`, so `task build` will emit broken absolute URLs.</violation>
</file>
<file name="docs/science/polynomial/4.md">
<violation number="1" location="docs/science/polynomial/4.md:73">
P2: The sum-of-fourth-powers formula is wrong: `3n^3` should be `3n^2`.</violation>
<violation number="2" location="docs/science/polynomial/4.md:274">
P2: This exercise answer ignores that the original five-person order is fixed, so `246` is incorrect.</violation>
<violation number="3" location="docs/science/polynomial/4.md:444">
P2: This interpolation definition uses the wrong point count and the wrong distinctness condition.</violation>
<violation number="4" location="docs/science/polynomial/4.md:461">
P2: The Lagrange interpolation formula drops the `i=0` term and omits one of the given points.</violation>
</file>
<file name="docs/science/polynomial/3.md">
<violation number="1" location="docs/science/polynomial/3.md:447">
P2: This recurrence rearrangement is incorrect: `b_n=n-3` implies `a_n=3a_{n-1}+n-3`, not `n+3`.</violation>
<violation number="2" location="docs/science/polynomial/3.md:538">
P2: No real characteristic roots do not imply the sequence is periodic; this statement overgeneralizes the recurrence theory.</violation>
<violation number="3" location="docs/science/polynomial/3.md:1443">
P2: `d_n` should be bounded below by `0`, not `1`; otherwise the squeeze argument is invalid.</violation>
<violation number="4" location="docs/science/polynomial/3.md:1498">
P2: This exponent transformation is incorrect: `(2021^{-2})^n` equals `2021^{-2n}`, not `2021^{-2^n}`.</violation>
</file>
<file name="docs/science/polynomial/6.md">
<violation number="1" location="docs/science/polynomial/6.md:59">
P2: Use `r \le n_i` here; the current condition incorrectly excludes valid cases with `r = n_i`.</violation>
<violation number="2" location="docs/science/polynomial/6.md:70">
P2: The summation bound should be `k`, not `n`; otherwise the constrained equation describes the wrong variables.</violation>
<violation number="3" location="docs/science/polynomial/6.md:181">
P2: This exact formula is false for derangements; use the nearest-integer form instead of `\lfloor n!/e \rfloor`.</violation>
</file>
<file name="docs/science/polynomial/5.md">
<violation number="1" location="docs/science/polynomial/5.md:128">
P2: This inclusion-exclusion example swaps `|A \cup B|` and `|A \cap B|`; `\lfloor 1000/15 \rfloor` is the intersection count.</violation>
<violation number="2" location="docs/science/polynomial/5.md:465">
P2: This count misses the choice of which two gaps 甲 and 乙 occupy, so the formula undercounts non-adjacent arrangements.</violation>
<violation number="3" location="docs/science/polynomial/5.md:874">
P2: For distinguishable people and identical balls, the partition `3,2,2` yields 3 assignments (choose which person gets 3), not 1.</violation>
</file>
<file name="docs/science/mathematics/2.md">
<violation number="1" location="docs/science/mathematics/2.md:157">
P2: This line defines well-foundedness too narrowly: it requires a minimal element of `S` itself instead of every non-empty subset of `S`.</violation>
<violation number="2" location="docs/science/mathematics/2.md:214">
P2: The maximal-element definition is incorrect for preorders; it rejects equivalent-but-distinct elements. Use `m\preceq a \implies a\preceq m` instead.</violation>
<violation number="3" location="docs/science/mathematics/2.md:386">
P2: These monotonicity laws are not bidirectional; `\iff` should be `\implies` here.</violation>
<violation number="4" location="docs/science/mathematics/2.md:427">
P2: This CNF example is malformed: the second clause starts with `\lor` and is missing its left operand.</violation>
</file>
<file name="docs/science/mathematics/1.md">
<violation number="1" location="docs/science/mathematics/1.md:15">
P2: This paragraph swaps `数字系统` and `记数系统`, contradicting the definitions introduced a few lines earlier.</violation>
<violation number="2" location="docs/science/mathematics/1.md:340">
P2: The manual Gray-code construction count is off: alternating these two moves needs `2^k - 1` transitions from the initial code, not `2^{k-1}`.</violation>
</file>
<file name="docs/home/roadmap.md">
<violation number="1" location="docs/home/roadmap.md:63">
P2: This resource is mislabeled as `群论`; the linked page is about graph matching (Hall 定理), not group theory.</violation>
</file>
Reply with feedback, questions, or to request a fix. Tag @cubic-dev-ai to re-run a review.
|
|
||
| 实际上，题型一中除以 $A(3,3)$ 的原因与此完全相同——题型一是题型二的一个特殊情况（所有人都拿到相同数量的球）。 | ||
|
|
||
| **情况三和四** 显然方案数为 $1$。 |
There was a problem hiding this comment.
P2: For distinguishable people and identical balls, the partition 3,2,2 yields 3 assignments (choose which person gets 3), not 1.
Prompt for AI agents
Check if this issue is valid — if so, understand the root cause and fix it. At docs/science/polynomial/5.md, line 874:
<comment>For distinguishable people and identical balls, the partition `3,2,2` yields 3 assignments (choose which person gets 3), not 1.</comment>
<file context>
@@ -1,402 +1,1064 @@
+
+ 实际上，题型一中除以 $A(3,3)$ 的原因与此完全相同——题型一是题型二的一个特殊情况（所有人都拿到相同数量的球）。
+
+ **情况三和四** 显然方案数为 $1$。
+
+ 完全不平均分配与题型二相同，只是所有人的球数都不一样，因此不需要除以任何排列数。
</file context>
|
|
||
| 以下逻辑表达式均为合取范式： | ||
|
|
||
| - $(\lnot A\lor\lnot B\lor C)\land(\lor D\lor\lnot E)$， |
There was a problem hiding this comment.
P2: This CNF example is malformed: the second clause starts with \lor and is missing its left operand.
Prompt for AI agents
Check if this issue is valid — if so, understand the root cause and fix it. At docs/science/mathematics/2.md, line 427:
<comment>This CNF example is malformed: the second clause starts with `\lor` and is missing its left operand.</comment>
<file context>
@@ -130,10 +130,435 @@ $$
+
+以下逻辑表达式均为合取范式：
+
+- $(\lnot A\lor\lnot B\lor C)\land(\lor D\lor\lnot E)$，
+- $(A\lor B)\land (C)$，
+- $(A\lor B)$，
</file context>
| - $(\lnot A\lor\lnot B\lor C)\land(\lor D\lor\lnot E)$， | |
| - $(\lnot A\lor\lnot B\lor C)\land(D\lor\lnot E)$， |
| 1. 翻转最低位得到下一个格雷码，（例如 $000\to 001$）； | ||
| 2. 把最右边的 $1$ 的左边的位翻转得到下一个格雷码，（例如 $001\to 011$）； | ||
|
|
||
| 交替按照上述策略生成 $2^{k-1}$ 次，可得到 $k$ 位的格雷码序列。 |
There was a problem hiding this comment.
P2: The manual Gray-code construction count is off: alternating these two moves needs 2^k - 1 transitions from the initial code, not 2^{k-1}.
Prompt for AI agents
Check if this issue is valid — if so, understand the root cause and fix it. At docs/science/mathematics/1.md, line 340:
<comment>The manual Gray-code construction count is off: alternating these two moves needs `2^k - 1` transitions from the initial code, not `2^{k-1}`.</comment>
<file context>
@@ -1,4 +1,432 @@
+ 1. 翻转最低位得到下一个格雷码，（例如 $000\to 001$）；
+ 2. 把最右边的 $1$ 的左边的位翻转得到下一个格雷码，（例如 $001\to 011$）；
+
+ 交替按照上述策略生成 $2^{k-1}$ 次，可得到 $k$ 位的格雷码序列。
+
+- 镜像构造：
</file context>
| 交替按照上述策略生成 $2^{k-1}$ 次，可得到 $k$ 位的格雷码序列。 | |
| 交替按照上述策略生成 $2^k-1$ 次，可得到 $k$ 位的格雷码序列。 |
![gemini-code-assist[bot]](https://avatars.githubusercontent.com/in/956858?s=60&v=4){kind=small}
There was a problem hiding this comment.
Code Review
This pull request introduces several structural and content updates, including the addition of a new Taskfile.yml, updates to the licensing information in README.md, and significant expansions to the mathematics and science documentation. The review feedback identified several technical inaccuracies in the mathematical content, specifically regarding calculus formulas, equivalent infinitesimals, and combinatorial identities, as well as some minor formatting and consistency issues. I have filtered out comments that were purely validation or lacked actionable suggestions, focusing on the identified technical errors.
|
|
||
| $$\begin{aligned}\sum_{k=1}^n\frac{1}{\sqrt{k} }&>\int_1^{n+1}\frac{1}{\sqrt{x} }\ dx=2\sqrt{x}|_1^{n+1}=2\left(\sqrt{n+1}-1\right)\\&<\int_0^n\frac{1}{\sqrt{x} }\ dx=2\sqrt{x}|_0^n=2\sqrt{n}\end{aligned}$$ | ||
|
|
||
| 练习 1：证明 $\displaystyle\sum_{k=2}^n\frac{1}{k\sqrt{k}}<\sqrt{2}\ \ \ \ \text{}$ 和 $\ \ \ \ \displaystyle\frac{2}{3}n^\frac{3}{2}\leq\sum_{k=1}^n\sqrt{k}\leq\frac{2}{3}[(n+1)^\frac{3}{2}-n]$ |
There was a problem hiding this comment.
练习1中的第二个不等式右侧可能存在笔误。根据标准积分放缩，$\sum_{k=1}^n\sqrt{k}<\int_1^{n+1} \sqrt{x} dx = \frac{2}{3}((n+1)^{3/2}-1)$。请检查此处的 -n 是否应为 -1。
docs/science/function/7.md
Outdated
| - **原函数的构造** | ||
| $$nf(x) + f'(x) = \frac{1}{e^{nx}}[e^{nx} f(x)]'$$ | ||
| $$f'(x)g(x) + f(x)g'(x) = [f(x)g(x)]'$$ | ||
| $$f'(x)g(x) - f(x)g'(x) = [\frac{f(x)}{g(x)}]'$$ |
There was a problem hiding this comment.
分式求导法则不正确。正确的公式是
| $$f'(x)g(x) - f(x)g'(x) = [\frac{f(x)}{g(x)}]'$$ | |
| $$[\frac{f(x)}{g(x)}]' = \frac{f'(x)g(x) - f(x)g'(x)}{[g(x)]^2}$$ |
| \begin{aligned} | ||
| y_1y_2&\le\left({y_1+y_2\over2}\right)^2\\ | ||
| x_1\dots x_{2n}&\le\left(x_1\dots x_n+x_{n+1}\dots x_{2n}\over2\right)^2\\ | ||
| &={(x_1\dots x_n)^2+(x_{n+1}+x_{2n})^2+2x_1\dots x_{2n}\over4}\\ | ||
| &={(x_1\dots x_n)^2+(x_{n+1}+x_{2n})^2\over2}\\ | ||
| &\le{(x_1+\dots+x_n)^{2n}+(x_{n+1}+\dots+x_{2n})^{2n}\over(2n)^{2n}}\\ | ||
| &\le\left({x_1+\dots+x_{2n}\over2n}\right)^{2n} | ||
| \end{aligned} | ||
| $$ |
There was a problem hiding this comment.
AM-GM 不等式反向归纳法中
标准证明思路如下：
由
令
则
由
因此
|
|
||
| 如对于集合 $\{0,1,2\}$ 的幂集 $S$ 和集合的包含关系 $\subseteq$，其对应的 Hasse 图为： | ||
|
|
||
| { width="70%" } |
There was a problem hiding this comment.
此处引用的图片 image.png 未在此次提交中添加，会导致图片无法显示。
| $$ | ||
| \boxed{C(n,m)={A(n,m)\over A(m,m)}={n!\over(n-m)!m!}} | ||
| (a+b)(a^2-ab+b^2)=a^3+b^3 | ||
| $$ | ||
|
|
||
| **性质**：$m!$ 整除任何连续的 $m$ 个整数的乘积。 | ||
|
|
||
| **证明**：通过构造组合数即可证明。对于任意连续的 $m$ 个整数 $n, n-1, \dots, n-m+1$，它们的乘积等于 $A(n,m)$，而 $C(n,m) = \frac{A(n,m)}{m!}$ 是一个整数，因此 $m!$ 必然整除 $A(n,m)$。 | ||
|
|
||
| ## 组合数的性质 | ||
|
|
||
| 组合数具有许多优良的性质，这些性质在计数问题中有着广泛的应用。下面我们逐一介绍这些性质。 | ||
|
|
||
| ### 基本性质 | ||
|
|
||
| 从组合数的定义可以直接得到以下性质： | ||
|
|
||
| $$ | ||
| \boxed{\tag1{n\choose m}={n\choose n-m}} | ||
| (a-b)(a^2+ab+b^2)=a^3-b^3 | ||
| $$ | ||
|
|
||
| 这个性质的组合意义是：从 $n$ 个元素中选出 $m$ 个，等价于选出 $n-m$ 个不选。 | ||
|
|
||
| 同样由定义可以推导出： | ||
|
|
||
| $$ | ||
| \boxed{{n\choose m}={n\over m}{n-1\choose m-1}\tag{1 II}} | ||
| x^3+\dfrac{1}{x^3}=\paren{x+\dfrac{1}{x}}\paren{x^2+\dfrac{1}{x^2}-1} | ||
| $$ | ||
|
|
||
| 这个公式在递推计算中非常有用。 | ||
|
|
||
| 另一个重要的恒等式是： | ||
| 一般的， | ||
|
|
||
| $$ | ||
| \boxed{{n\choose m}{m\choose k}={n\choose k}{n-k\choose m-k}}\tag{1 III} | ||
| a^n-b^n=(a-b)(a^{n-1}+a^{n-2}b+\dots+b^{n-1}) | ||
| $$ | ||
|
|
||
| 这个等式的组合意义是：从 $n$ 个中选 $m$ 个，再从 $m$ 个中选 $k$ 个，等价于先从 $n$ 个中直接选 $k$ 个，然后再从剩下的 $n-k$ 个中补选 $m-k$ 个。 | ||
|
|
||
| ### 递推关系 | ||
|
|
||
| 组合数满足一个经典的递推公式： | ||
|
|
||
| $$ | ||
| \boxed{\tag2{n\choose m}={n-1\choose m}+{n-1\choose m-1}} | ||
| a^n+b^n=(a+b)(a^{n-1}-a^{n-2}b+\dots\pm b^{n-1}),n\equiv1\pmod2 | ||
| $$ | ||
|
|
||
| 这个递推式的组合意义是：考虑 $n$ 个元素中的某个特定元素，将所有方案分为两类——选这个元素和不选这个元素，分别对应右边的两项。这个递推式在计算组合数和裂项求和中非常有用。 | ||
|
|
||
| 类似地，排列数也有对应的递推式： | ||
| 双十字相乘： | ||
|
|
There was a problem hiding this comment.
这部分关于微分方程的内容出现在“组合数学”和“排列数”的章节中，内容上不相关，可能是编辑错误，建议移至更合适的位置。
|
|
||
| 此外，我们有一个关于补数和无限循环小数的有趣定理：Midy 定理指出，设 $a$ 是正整数，$p$ 是正素数，$a/p$ 在 $b$ 进制下的表示为 $0.\overline{a_1a_2\cdots a_l}$，其中 $l$ 为（最短）循环节长度。若 $l$ 是偶数，设 $l=2k$，则 $a_1a_2\cdots a_k$ 是 $a_{k+1}a_{k+2}\cdots a_{2k}$ 的减补数，即： | ||
|
|
||
| - $a_i+a_{i+k}=b$， |
There was a problem hiding this comment.
Midy 定理的内容有误。当循环节长度
| - $a_i+a_{i+k}=b$， | |
| - $a_i+a_{i+k}=b-1$, |
docs/science/polynomial/1.md
Outdated
| 容易发现， | ||
|
|
||
| $$ | ||
| 2S=1+{1\over2}-{1\over n+1}-{1\over n-2} |
There was a problem hiding this comment.
裂项求和的结果有误。消项后剩下的负数项应该是
| 2S=1+{1\over2}-{1\over n+1}-{1\over n-2} | |
| 2S=1+{1\over2}-{1\over n+1}-{1\over n+2} |
![devin-ai-integration[bot]](https://avatars.githubusercontent.com/in/811515?s=60&v=4){kind=small}
|
|
||
| 以下逻辑表达式均为合取范式： | ||
|
|
||
| - $(\lnot A\lor\lnot B\lor C)\land(\lor D\lor\lnot E)$， |
There was a problem hiding this comment.
🟡 Stray \lor operator with no left operand in CNF example
In the conjunctive normal form (CNF) example, the second clause (\lor D\lor\lnot E) has a leading \lor with no left operand, making the expression syntactically invalid. It should be (D\lor\lnot E) or similar. This is a typo introduced in the new Boolean algebra section.
| - $(\lnot A\lor\lnot B\lor C)\land(\lor D\lor\lnot E)$， | |
| - $(\lnot A\lor\lnot B\lor C)\land(D\lor\lnot E)$， |
Was this helpful? React with 👍 or 👎 to provide feedback.
docs/science/polynomial/1.md
Outdated
| 2a_{n-1}=4a_{n-1}+2\\ | ||
| 4a_{n=2}=8a_{n-2}+4\\ |
There was a problem hiding this comment.
🔴 Two incorrect subscripts in 变形累加 derivation
The derivation at docs/science/polynomial/1.md:1283-1285 has two subscript errors that make the algebraic steps logically wrong:
Detailed error breakdown
- Line 1284:
2a_{n-1}=4a_{n-1}+2— the right-hand side subscript{n-1}should be{n-2}. The step is multiplying the recurrence for$a_{n-1}$ by 2, yielding$2a_{n-1} = 4a_{n-2} + 2$ . - Line 1285:
4a_{n=2}=8a_{n-2}+4— the left subscript{n=2}is a typo for{n-2}(equals sign instead of minus), and the right subscript{n-2}should be{n-3}. The correct equation is$4a_{n-2} = 8a_{n-3} + 4$ .
| 2a_{n-1}=4a_{n-1}+2\\ | |
| 4a_{n=2}=8a_{n-2}+4\\ | |
| 2a_{n-1}=4a_{n-2}+2\\ | |
| 4a_{n-2}=8a_{n-3}+4\\ |
Was this helpful? React with 👍 or 👎 to provide feedback.
Co-authored-by: cubic-dev-ai[bot] <191113872+cubic-dev-ai[bot]@users.noreply.github.com> Co-authored-by: gemini-code-assist[bot] <176961590+gemini-code-assist[bot]@users.noreply.github.com> Co-authored-by: devin-ai-integration[bot] <158243242+devin-ai-integration[bot]@users.noreply.github.com>
This comment was marked as resolved.
This comment was marked as resolved.
Sorry, something went wrong.
Co-authored-by: cubic-dev-ai[bot] <191113872+cubic-dev-ai[bot]@users.noreply.github.com>
![kilo-code-bot[bot]](https://avatars.githubusercontent.com/in/2193792?s=60&v=4){kind=small}
|
|
||
| ### 极限定义 | ||
|
|
||
| 对于函数 $f(x)$ 与实数 $a$，如果存在实数 $b$，使得 $\forall \varepsilon > 0$，$\exist \delta > 0$，对任意 $x \in (a - \delta, a) \cup (a, a + \delta)$，有 $|f(x) - b| < \varepsilon$，则 $b$ 称作 $f(x)$ 在点 $a$ 的极限，记作 |
There was a problem hiding this comment.
SUGGESTION: Typo in LaTeX command - should be \exists instead of \exist
| 对于函数 $f(x)$ 与实数 $a$，如果存在实数 $b$，使得 $\forall \varepsilon > 0$，$\exist \delta > 0$，对任意 $x \in (a - \delta, a) \cup (a, a + \delta)$，有 $|f(x) - b| < \varepsilon$，则 $b$ 称作 $f(x)$ 在点 $a$ 的极限，记作 | |
| 对于函数 $f(x)$ 与实数 $a$，如果存在实数 $b$，使得 $\forall \varepsilon > 0$，$\exists \delta > 0$，对任意 $x \in (a - \delta, a) \cup (a, a + \delta)$，有 $|f(x) - b| < \varepsilon$，则 $b$ 称作 $f(x)$ 在点 $a$ 的极限，记作 |
Code Review SummaryStatus: 1 Issue Found | Recommendation: Address before merge Overview
Issue Details (click to expand)SUGGESTION
Other Observations (not in diff)Issues found in unchanged code that cannot receive inline comments:
Files Reviewed (17 files)
The PR overall looks good. It reorganizes math docs, adds new calculus content, and replaces Makefile with Taskfile.yml. The main actionable item is the LaTeX typo fix. The missing Makefile commands and the roadmap URLs are noted for awareness but don't block merge. Reviewed by minimax-m2.5-20260211 · 1,465,800 tokens |
| $$ | ||
| f'(x)+p(x)f(x)>q(x) | ||
| $$ | ||
|
|
||
| 我们先简单说一下简单的微分方程怎么解，我们将式子最终化为： | ||
|
|
||
| $$ | ||
| u(x)\d x=v(y)\d y | ||
| $$ | ||
|
|
||
| 然后两边求积分，化简即可。 |
There was a problem hiding this comment.
🔴 Content corruption: differential equation content incorrectly spliced into combinatorics permutation section
In the reorganized docs/science/polynomial/5.md, the permutation number derivation section contains content from an unrelated differential equations / calculus source. After the introductory text "我们来推导排列数的计算公式。按照排列的定义，我们依次分析第 f'(x)+p(x)f(x)>q(x) and differential equation solving techniques instead of the original permutation step table and formula derivation. The same issue recurs at docs/science/polynomial/5.md:320-335 where the summation properties section ("下面是一个利用裂项技巧的求和恒等式") shows f'(x)+p(x)f(x)=0 and dy/dx+p(x)y=0 instead of the actual combinatorics identity proof. Additionally, an admonition block opened at line 178 is never properly closed, causing downstream rendering issues.
Corrupted content at line 165 (should be permutation table)
The current content reads:
$$
f'(x)+p(x)f(x)>q(x)
$$
我们先简单说一下简单的微分方程怎么解
The original (correct) content had a table showing step-by-step selection counts and the formula A(n,m) = n(n-1)...(n-m+1).
Prompt for agents
The file docs/science/polynomial/5.md has content corruption at multiple locations where content from a differential equations / calculus source was incorrectly merged into the combinatorics file. The key affected regions are:
1. Lines 165-187: The permutation derivation section (排列数) was replaced with differential equation content (f'(x)+p(x)f(x)>q(x), u(x)dx=v(y)dy). The original content had a table showing step-by-step selection counts and the derivation of A(n,m). An admonition block opened at line 178 is also never closed.
2. Lines 320-335: The summation properties proof section was replaced with ODE content (f'(x)+p(x)f(x)=0, dy/dx+p(x)y=0, ln y=-P(x)+C). The original had the proof of the summation identity using the telescoping technique.
3. Lines 1040-1064: End of file has calculus content about parameter analysis and inequality proofs that doesn't belong in a combinatorics chapter.
To fix: Restore the original permutation derivation table and formula, the summation identity proof, and remove the misplaced calculus/DE content. The correct content for these sections can be found in the git history of the old docs/science/polynomial/4.md file.
Was this helpful? React with 👍 or 👎 to provide feedback.
| 二项式定理（Binomial Theorem）是组合数学中最核心的定理之一，它建立了多项式展开与组合数之间的桥梁。其基本形式为： | ||
| 而只有搞明白这类问题，才能在组合数学上继续深入。 | ||
|
|
||
| </center> |
There was a problem hiding this comment.
🟡 Orphaned </center> tag without matching opening <center>
The old polynomial/4.md had <center markdown> before the introductory text block. During the reorganization to polynomial/5.md, the opening <center markdown> tag was removed but the closing </center> at line 9 was left behind. This orphaned closing tag will either render as raw HTML or cause unexpected layout behavior.
| </center> |
Was this helpful? React with 👍 or 👎 to provide feedback.
|
|
||
| 因此不难得出 $\{f^{-1}(\{i\}):1\leq i\leq d\}$ 是一个反链覆盖，从而最小反链覆盖数至多为 $d$. | ||
|
|
||
| Dilworth 定理与 [Hall 婚配定理](../graph/graph-matching/graph-match.md#hall-定理) 等价。我们可以用 Dilworth 定理证明如下定理： |
There was a problem hiding this comment.
🟡 Broken cross-reference to non-existent graph/ directory
The newly added content links to [Hall 婚配定理](../graph/graph-matching/graph-match.md#hall-定理), which resolves to docs/science/graph/graph-matching/graph-match.md. However, the docs/science/graph/ directory does not exist in the repository, making this a dead link that will produce a 404 error.
Prompt for agents
In docs/science/mathematics/2.md line 299, there is a markdown link to ../graph/graph-matching/graph-match.md#hall-定理 but the docs/science/graph/ directory does not exist in the repository. Either create the referenced file, update the link to point to an existing page that discusses Hall's theorem, or replace the link with a plain text reference or an external link (e.g., to the corresponding OI-Wiki page or Wikipedia article on Hall's marriage theorem).
Was this helpful? React with 👍 or 👎 to provide feedback.
1 participant
Summary by cubic
Reorganized math docs by merging sequences/combinatorics into
science/polynomial/1..6, expanded the new calculus chapter inscience/function/7.md, and replaced theMakefilewith aTaskfile.yml. Updated licensing to CC BY‑SA 4.0 and cleaned up captions/notes and the double‑slit section.New Features
Taskfile.yml(build, submodule update/sync, onstart) usinguv run scripts/generate.py; removedMakefile.science/polynomial/1..6; removedscience/sequence/*.science/function/7.md(limits & calculus); renamed sidebars to “数列与组合数学” and “函数导数微积分”.science/mathematics/1.md,2.md, new SVG).science/modern/3.md); cleaned captions/alt text across pages; added roadmap links.README.mdandproject.json.Migration
task buildinstead ofmake(optionalSITE_URLinTaskfile.yml).task sub-update/task sub-sync; runtask onstartwhen needed.task build(oruv run scripts/generate.py --build --site_url=...).Written for commit 12fceef. Summary will update on new commits.