math-review
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ChineseTable of Contents
目录
- Quick Start
- When to Use
- Required TodoWrite Items
- Core Workflow
- 1. Context Sync
- 2. Requirements Mapping
- 3. Derivation Verification
- 4. Stability Assessment
- 5. Proof of Work
- Progressive Loading
- Essential Checklist
- Output Format
- Summary
- Context
- Requirements Analysis
- Derivation Review
- Stability Analysis
- Issues
- Recommendation
- Exit Criteria
Mathematical Algorithm Review
数学算法审查
Intensive analysis ensuring numerical stability and alignment with standards.
通过深度分析确保数值稳定性并符合相关标准。
Quick Start
快速开始
bash
/math-reviewVerification: Run the command with flag to verify availability.
--helpbash
/math-review验证方式： 运行带参数的命令以确认技能可用。
--helpWhen To Use
适用场景
- Changes to mathematical models or algorithms
- Statistical routines or probabilistic logic
- Numerical integration or optimization
- Scientific computing code
- ML/AI model implementations
- Safety-critical calculations
- 数学模型或算法变更
- 统计程序或概率逻辑
- 数值积分或优化
- 科学计算代码
- ML/AI模型实现
- 安全关键型计算
When NOT To Use
不适用场景
- General algorithm review - use architecture-review
- Performance optimization - use parseltongue:python-performance
- General algorithm review - use architecture-review
- Performance optimization - use parseltongue:python-performance
- 通用算法审查 - use architecture-review
- 性能优化 - use parseltongue:python-performance
- 通用算法审查 - use architecture-review
- 性能优化 - use parseltongue:python-performance
Required TodoWrite Items
所需TodoWrite事项
math-review:context-syncedmath-review:requirements-mappedmath-review:derivations-verifiedmath-review:stability-assessedmath-review:evidence-logged
math-review:context-syncedmath-review:requirements-mappedmath-review:derivations-verifiedmath-review:stability-assessedmath-review:evidence-logged
Core Workflow
核心工作流
1. Context Sync
1. 上下文同步
bash
pwd && git status -sb && git diff --stat origin/main..HEADVerification: Run to confirm working tree state.
Enumerate math-heavy files (source, tests, docs, notebooks). Classify risk: safety-critical, financial, ML fairness.
git statusbash
pwd && git status -sb && git diff --stat origin/main..HEAD验证方式： 运行确认工作树状态。
列出涉及大量数学运算的文件（源码、测试、文档、笔记本）。进行风险分类：安全关键型、金融类、ML公平性相关。
git status2. Requirements Mapping
2. 需求映射
Translate requirements → mathematical invariants. Document pre/post conditions, conservation laws, bounds. Load:
modules/requirements-mapping.md将需求转化为数学不变量。记录前置/后置条件、守恒定律、边界条件。加载模块：
modules/requirements-mapping.md3. Derivation Verification
3. 推导验证
Re-derive formulas using CAS. Challenge approximations. Cite authoritative standards (NASA-STD-7009, ASME VVUQ). Load:
modules/derivation-verification.md使用CAS重新推导公式。质疑近似假设。引用权威标准（NASA-STD-7009、ASME VVUQ）。加载模块：
modules/derivation-verification.md4. Stability Assessment
4. 稳定性评估
Evaluate conditioning, precision, scaling, randomness. Compare complexity. Quantify uncertainty. Load:
modules/numerical-stability.md评估条件数、精度、缩放、随机性。比较复杂度。量化不确定性。加载模块：
modules/numerical-stability.md5. Proof of Work
5. 工作成果验证
bash
pytest tests/math/ --benchmark
jupyter nbconvert --execute derivation.ipynbVerification: Run to verify.
Log deviations, recommend: Approve / Approve with actions / Block. Load:
pytest -v tests/math/modules/testing-strategies.mdbash
pytest tests/math/ --benchmark
jupyter nbconvert --execute derivation.ipynb验证方式： 运行进行验证。
记录偏差，给出建议：批准/附条件批准/阻止。加载模块：
pytest -v tests/math/modules/testing-strategies.mdProgressive Loading
渐进式加载
Default (200 tokens): Core workflow, checklists
+Requirements (+300 tokens): Invariants, pre/post conditions, coverage analysis
+Derivation (+350 tokens): CAS verification, standards, citations
+Stability (+400 tokens): Numerical properties, precision, complexity
+Testing (+350 tokens): Edge cases, benchmarks, reproducibility
Total with all modules: ~1600 tokens
默认（200 tokens）： 核心工作流、检查清单
+需求映射（+300 tokens）： 不变量、前置/后置条件、覆盖分析
+推导验证（+350 tokens）： CAS验证、标准、引用
+稳定性评估（+400 tokens）： 数值属性、精度、复杂度
+测试（+350 tokens）： 边缘案例、基准测试、可复现性
加载所有模块总token数： ~1600
Essential Checklist
必备检查清单
Correctness: Formulas match spec | Edge cases handled | Units consistent | Domain enforced
Stability: Condition number OK | Precision sufficient | No cancellation | Overflow prevented
Verification: Derivations documented | References cited | Tests cover invariants | Benchmarks reproducible
Documentation: Assumptions stated | Limitations documented | Error bounds specified | References linked
正确性： 公式符合规格 | 处理边缘案例 | 单位一致 | 域约束生效
稳定性： 条件数正常 | 精度足够 | 无抵消误差 | 防止溢出
验证： 推导过程已记录 | 引用参考资料 | 测试覆盖不变量 | 基准测试可复现
文档： 明确假设条件 | 记录局限性 | 说明误差范围 | 链接参考资料
Output Format
输出格式
markdown
undefinedmarkdown
undefinedSummary
摘要
[Brief findings]
[简要发现]
Context
上下文
Files | Risk classification | Standards
文件 | 风险分类 | 标准
Requirements Analysis
需求分析
| Invariant | Verified | Evidence |
| 不变量 | 已验证 | 证据 |
Derivation Review
推导审查
[Status and conflicts]
[状态与冲突]
Stability Analysis
稳定性分析
Condition number | Precision | Risks
条件数 | 精度 | 风险
Issues
问题
[M1] [Title]: Location | Issue | Fix
[M1] [标题]: 位置 | 问题描述 | 修复方案
Recommendation
建议
Approve / Approve with actions / Block
**Verification:** Run the command with `--help` flag to verify availability.批准/附条件批准/阻止
**验证方式：** 运行带`--help`参数的命令以确认技能可用。Exit Criteria
退出标准
- Context synced, requirements mapped, derivations verified, stability assessed, evidence logged with citations
- 已完成上下文同步、需求映射、推导验证、稳定性评估，并记录带引用的证据
Troubleshooting
故障排除
Common Issues
常见问题
Command not found
Ensure all dependencies are installed and in PATH
Permission errors
Check file permissions and run with appropriate privileges
Unexpected behavior
Enable verbose logging with flag
--verbose命令未找到
确保所有依赖已安装且在PATH中
权限错误
检查文件权限并使用适当权限运行
异常行为
使用参数启用详细日志
--verbose