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
1---2name: research-543description: 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.4---5
6# Technical Research
7
8## Purpose
9
10Conduct thorough, structured research to inform design and implementation decisions. Produce actionable findings with clear sources, not just raw information dumps.
11
12## When to Use
13
14- Investigating an algorithm or method before implementing it
15- Comparing competing approaches (solvers, formulations, libraries)
16- Finding reference implementations or validation data
17- Understanding a mathematical formulation from the literature
18- Evaluating whether an external package meets requirements
19
20## Process
21
22### 1. Define the Research Question
23
24Clarify with the user:
25- What specific question needs answering?
26- What decisions will this research inform?
27- Are there known starting points (papers, packages, textbooks)?
28- What constraints matter (performance, accuracy, AD-compatibility, license)?
29
30### 2. Search Strategy
31
32Execute multiple search angles:
33- **Academic/algorithmic**: search for papers, textbook references, survey articles
34- **Implementation**: search for existing Julia packages, GitHub repos, reference code
35- **Community**: search Julia Discourse, relevant forums, package documentation
36- **Comparison**: search for benchmarks, trade-off analyses, known limitations
37
38Formulate 3-5 query variations per angle for coverage.
39
40### 3. Evaluate Sources
41
42For each source found:
43- **Relevance**: Does it directly address the research question?
44- **Authority**: Is it a peer-reviewed paper, official docs, or a blog post?
45- **Recency**: Is the information current? Are there newer approaches?
46- **Applicability**: Does it match our constraints (Julia, AD-compatible, etc.)?
47
48### 4. Synthesize Findings
49
50Organize results into a structured summary:
51
52```markdown
53## Research: [Topic]
54
55### Question
56[The specific question being investigated]
57
58### Key Findings
59- Finding 1 (with source)
60- Finding 2 (with source)
61
62### Approaches Compared
63| Approach | Pros | Cons | Source |
64|----------|------|------|--------|
65| ... | ... | ... | ... |
66
67### Recommendation
68[Clear recommendation with rationale]
69
70### Open Questions
71[Anything unresolved that needs further investigation]
72
73### References
741. [Author, Title, Year, URL/DOI]
75```
76
77### 5. Verify Key Claims
78
79- Cross-reference important claims across multiple sources
80- Flag contradictions or disagreements in the literature
81- Note where consensus exists vs. active debate
82
83## Output Requirements
84
85- Always provide source URLs or citations for claims
86- Use direct quotes for important technical statements
87- Clearly distinguish established facts from opinions/recommendations
88- Identify gaps where information is missing or uncertain
89- End with actionable next steps
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