Table of Contents
Mathematical Algorithm Review
Intensive analysis ensuring numerical stability and alignment with standards.
Quick Start
Verification: Run the command with
flag to verify availability.
When To Use
- 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
When NOT To Use
- General algorithm review -
use architecture-review
- Performance optimization - use parseltongue:python-performance
- General algorithm review -
use architecture-review
- Performance optimization - use parseltongue:python-performance
Required TodoWrite Items
math-review:context-synced
math-review:requirements-mapped
math-review:derivations-verified
math-review:stability-assessed
math-review:evidence-logged
Core Workflow
1. Context Sync
bash
pwd && git status -sb && git diff --stat origin/main..HEAD
Verification: Run
to confirm working tree state.
Enumerate math-heavy files (source, tests, docs, notebooks). Classify risk: safety-critical, financial, ML fairness.
2. Requirements Mapping
Translate requirements → mathematical invariants. Document pre/post conditions, conservation laws, bounds.
Load:
modules/requirements-mapping.md
3. Derivation Verification
Re-derive formulas using CAS. Challenge approximations. Cite authoritative standards (NASA-STD-7009, ASME VVUQ).
Load:
modules/derivation-verification.md
4. Stability Assessment
Evaluate conditioning, precision, scaling, randomness. Compare complexity. Quantify uncertainty.
Load:
modules/numerical-stability.md
5. Proof of Work
bash
pytest tests/math/ --benchmark
jupyter nbconvert --execute derivation.ipynb
Verification: Run
to verify.
Log deviations, recommend: Approve / Approve with actions / Block.
Load:
modules/testing-strategies.md
Progressive Loading
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
Essential Checklist
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
Output Format
markdown
## Summary
[Brief findings]
## Context
Files | Risk classification | Standards
## Requirements Analysis
| Invariant | Verified | Evidence |
## Derivation Review
[Status and conflicts]
## Stability Analysis
Condition number | Precision | Risks
## Issues
[M1] [Title]: Location | Issue | Fix
## Recommendation
Approve / Approve with actions / Block
Verification: Run the command with
flag to verify availability.
Exit Criteria
- Context synced, requirements mapped, derivations verified, stability assessed, evidence logged with citations
Troubleshooting
Common Issues
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