math-reasoning

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🇺🇸

Original

English

🇨🇳

Translation

Chinese

Mathematical Reasoning

数学推理

Perform rigorous mathematical reasoning and produce publication-quality LaTeX output.

执行严谨的数学推理并生成达到出版级别的LaTeX输出。

Input

输入

$0

— Task type:

derive

prove

formalize

stats

notation

verify

```
$1
```
— Context: equation, theorem statement, problem description, or data description

```
$0
```
— 任务类型：
```
derive
```
（推导）、
```
prove
```
（证明）、
```
formalize
```
（形式化）、
```
stats
```
（统计）、
```
notation
```
（符号）、
```
verify
```
（验证）
```
$1
```
— 上下文：方程、定理陈述、问题描述或数据描述

Tasks

任务

derive

— Step-by-step equation derivation

derive

— 分步方程推导

Show every intermediate step. Justify each with the rule applied. Box final result with

\boxed{}

. Number important equations with

\label{eq:name}

展示每一个中间步骤。用所应用的规则为每一步提供依据。用

\boxed{}

框住最终结果。为重要方程编号，格式为

\label{eq:name}

。

prove

— Formal theorem proof

prove

— 正式定理证明

Use appropriate technique: direct, contradiction, induction, construction, or cases. See

references/proof-templates.md

for LaTeX templates.

使用合适的方法：直接证明、反证法、归纳法、构造法或分情况讨论。可参考

references/proof-templates.md

中的LaTeX模板。

formalize

— Problem setting formalization

formalize

— 问题设定形式化

Convert informal description into formal mathematical framework with: variable definitions, domain/range specifications, assumptions, objective function.

将非正式描述转换为正式的数学框架，包括：变量定义、定义域/值域说明、假设条件、目标函数。

stats

— Statistical test selection

stats

— 统计检验选择

Use the decision tree in

references/notation-guide.md

to select appropriate tests. Report p-values, effect sizes, confidence intervals.

使用

references/notation-guide.md

中的决策树选择合适的检验方法。报告p值、效应量、置信区间。

notation

— Generate notation table

notation

— 生成符号表

Create a

\begin{table}

with all symbols used in the paper. Use standard ML notation from

references/notation-guide.md

创建一个

\begin{table}

环境，列出论文中使用的所有符号。使用

references/notation-guide.md

中的标准ML符号。

verify

— Check mathematical correctness

verify

— 检查数学正确性

Verify: dimensional consistency, boundary cases, gradient computations, notation consistency across sections.

验证：维度一致性、边界情况、梯度计算、各章节间的符号一致性。

References

参考资料

Standard ML notation + statistical tests:

~/.claude/skills/math-reasoning/references/notation-guide.md

Proof templates and theorem environments:

~/.claude/skills/math-reasoning/references/proof-templates.md

标准ML符号 + 统计检验：

~/.claude/skills/math-reasoning/references/notation-guide.md

证明模板和定理环境：

~/.claude/skills/math-reasoning/references/proof-templates.md

Rules

规则

Define ALL symbols before first use: "Let $\mathcal{X}$ denote..."
Use consistent notation throughout the paper
Number equations that are referenced later
Use
```
\tag{reason}
```
for key derivation steps
State assumptions explicitly
Cite lemmas and prior results used in proofs

所有符号在首次使用前必须定义：“令$\mathcal{X}$表示...”
整篇论文中使用一致的符号
为后续会引用的方程编号
对关键推导步骤使用
```
\tag{reason}
```
明确陈述假设条件
在证明中引用所使用的引理和先前结果

math-reasoning

Original

Translation

Mathematical Reasoning

数学推理

Input

输入

Tasks

任务

`derive`
— Step-by-step equation derivation

`derive`
— 分步方程推导

`prove`
— Formal theorem proof

`prove`
— 正式定理证明

`formalize`
— Problem setting formalization

`formalize`
— 问题设定形式化

`stats`
— Statistical test selection

`stats`
— 统计检验选择

`notation`
— Generate notation table

`notation`
— 生成符号表

`verify`
— Check mathematical correctness

`verify`
— 检查数学正确性

References

参考资料

Rules

规则

Related Skills

相关技能