research

name	research
description	Systematic technical and scientific research for algorithms, papers, libraries, and implementation strategies. Use when investigating new algorithms, comparing approaches, finding reference implementations, reviewing literature, or gathering information before design decisions.

Technical Research

Purpose

Conduct thorough, structured research to inform design and implementation decisions. Produce actionable findings with clear sources, not just raw information dumps.

When to Use

• Investigating an algorithm or method before implementing it
• Comparing competing approaches (solvers, formulations, libraries)
• Finding reference implementations or validation data
• Understanding a mathematical formulation from the literature
• Evaluating whether an external package meets requirements

Process

1. Define the Research Question

Clarify with the user:

• What specific question needs answering?
• What decisions will this research inform?
• Are there known starting points (papers, packages, textbooks)?
• What constraints matter (performance, accuracy, AD-compatibility, license)?

2. Search Strategy

Execute multiple search angles:

• Academic/algorithmic: search for papers, textbook references, survey articles
• Implementation: search for existing Julia packages, GitHub repos, reference code
• Community: search Julia Discourse, relevant forums, package documentation
• Comparison: search for benchmarks, trade-off analyses, known limitations

Formulate 3-5 query variations per angle for coverage.

3. Evaluate Sources

For each source found:

• Relevance: Does it directly address the research question?
• Authority: Is it a peer-reviewed paper, official docs, or a blog post?
• Recency: Is the information current? Are there newer approaches?
• Applicability: Does it match our constraints (Julia, AD-compatible, etc.)?

4. Synthesize Findings

Organize results into a structured summary:

## Research: [Topic]

### Question
[The specific question being investigated]

### Key Findings
- Finding 1 (with source)
- Finding 2 (with source)

### Approaches Compared
| Approach | Pros | Cons | Source |
|----------|------|------|--------|
| ...      | ...  | ...  | ...    |

### Recommendation
[Clear recommendation with rationale]

### Open Questions
[Anything unresolved that needs further investigation]

### References
1. [Author, Title, Year, URL/DOI]

5. Verify Key Claims

• Cross-reference important claims across multiple sources
• Flag contradictions or disagreements in the literature
• Note where consensus exists vs. active debate

Output Requirements

• Always provide source URLs or citations for claims
• Use direct quotes for important technical statements
• Clearly distinguish established facts from opinions/recommendations
• Identify gaps where information is missing or uncertain
• End with actionable next steps