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math-reasoning

该 Skill 针对研究论文提供分步公式推导、形式化定理证明、问题设定形式化、统计检验选择、符号表生成和数学正确性检查，并输出规范的 LaTeX 数学记号。它依赖内置参考文档，适合学术写作中的数学表达与论证整理。

lingzhi227
热度 0.00
最近更新 2026-10-19 01:34:55
分类：知识依赖：纯提示词应用场景：研究 / 概念解释 / 模板

安装技能

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执行命令安装此 skill： npx secure-skills-cli add lingzhi227/agent-research-skills/math-reasoning
Metadata
name
math-reasoning
description
Formal mathematical reasoning for research papers — derive equations, write proofs, formalize problem settings, select statistical tests, and generate LaTeX math notation. Use when the user needs mathematical derivations, theorem proofs, notation tables, or statistical analysis formalization.
argument-hint
["task-or-context"]

Mathematical Reasoning

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

Input

  • $0 — Task type: derive, prove, formalize, stats, notation, verify
  • $1 — Context: equation, theorem statement, problem description, or data description

Tasks

derive — Step-by-step equation derivation

Show every intermediate step. Justify each with the rule applied. Box final result with \boxed{}. Number important equations with \label{eq:name}.

prove — Formal theorem proof

Use appropriate technique: direct, contradiction, induction, construction, or cases. See references/proof-templates.md for LaTeX templates.

formalize — Problem setting formalization

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

stats — Statistical test selection

Use the decision tree in references/notation-guide.md to select appropriate tests. Report p-values, effect sizes, confidence intervals.

notation — Generate notation table

Create a \begin{table} with all symbols used in the paper. Use standard ML notation from references/notation-guide.md.

verify — Check mathematical correctness

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

References

  • 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

Rules

  • 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

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