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Contour Integrals · vibeeval | DecimalAI

scienceby vibeeval

Contour Integrals

vibeeval/contour-integrals

Source vibeeval/vibecosystem ↗License MIT

Problem-solving strategies for contour integrals in complex analysis

SkillScore100Maintained

Automatic

Tutoring & Education pack

Last verified 8/3/2026

What it changes

Passed 22 of 22 test cases with the skill, and 20 of 22 without it.

Without skill91%

With skill100%

Checks it passed that the model alone missed

Uses the residue subcommand with --var z and --at I
Uses the integrate subcommand with --from -oo and --to oo

2 fixed20 passed either way0 still failing0 broke

Pass-rate lift: +9 pp
Tokens: +38%
Agent turns: 0%
Response time: -27%

Model gemini-3.6-flashMeasured 8/3/2026v122 of 22 cases passed with skill

Tokens, turns and time describe resource use, not a dollar price.

Use this skill

Save it into your project's skills folder. Claude Code picks it up in its next session.

curl -fsSL --create-dirs -o .claude/skills/vibeeval-contour-integrals/SKILL.md https://app.decimal.ai/s/vibeeval-contour-integrals/SKILL.md

Want it pinned and updatable? pip install "decimalai>=0.15", then decimalai skills add vibeeval-contour-integrals, and start Claude Code with claude --plugin-dir "$(git rev-parse --show-toplevel)/.agents"

1 · One-time — install the CLI (docs ↗)

pip install "decimalai>=0.15"

2 · Get the skill — writes .agents/skills/vibeeval-contour-integrals/ and pins it in .decimal/skills.lock

decimalai skills add vibeeval-contour-integrals

No CLI? Get the same file — curl · raw file

curl -fsSL --create-dirs -o .claude/skills/vibeeval-contour-integrals/SKILL.md https://app.decimal.ai/s/vibeeval-contour-integrals/SKILL.md

Raw file: /s/vibeeval-contour-integrals/SKILL.md ↗ · machine-readable summary at /s/vibeeval-contour-integrals.json ↗

Safety checks: 3 of 3 passed

Code scan CleanIntent PassedContent Clean

See it in action

One of 2 test cases the skill fixed. Same model, same prompt, with and without the skill.

1 of 2

Prompt

Write the CLI invocation using the runtime harness python entrypoint to compute the residue of 1/(z**2 + 1) with respect to variable z at point I.

What was checked, without and with the skill
Checked	Without skill	With skill
Uses the residue subcommand with --var z and --at I	Missed	Passed

case-10 · gemini-3.6-flash · 8/3/2026 · answers are capped and redacted

What's inside

The instructions your model reads when the skill loads.

SKILL.md64 linessingle file

Contour Integrals

When to Use

Use this skill when working on contour-integrals problems in complex analysis.

Decision Tree

Integral Type Selection
- For integral_{-inf}^{inf} f(x)dx where f decays like 1/x^a, a > 1:
  - Use semicircular contour (upper or lower half-plane)
- For integral involving e^{ix} or trigonometric functions:
  - Close in upper half-plane for e^{ix} (Jordan's lemma)
  - Close in lower half-plane for e^{-ix}
- For integral_0^{2pi} f(cos theta, sin theta)d theta:
  - Substitute z = e^{i theta}, use unit circle contour
- For integrand with branch cuts:
  - Use keyhole or dogbone contour around cuts
Contour Setup
- Identify singularities and their locations
- Choose contour that encloses desired singularities
- sympy_compute.py solve "f(z) = inf" to find poles
Jordan's Lemma
- For integral over semicircle of radius R:
- If |f(z)| -> 0 as |z| -> inf, semicircular contribution vanishes
Compute with Residue Theorem
- oint_C f(z)dz = 2pii * (sum of residues inside C)
- sympy_compute.py residue "f(z)" --var z --at z0

Tool Commands

Sympy_Residue

uv run python -m runtime.harness scripts/sympy_compute.py residue "1/(z**2 + 1)" --var z --at I

Track record

Benchmark

22 / 22

test cases passed, vs 20 / 22 without

Adoption

Users: 0
Times used: 0

Safety and source details

SkillSafety

✓ 3 of 3 passed

Code scan15 of 15 checks clean

0 critical · 0 warning · 0 info — scanner v4 — 8/1/2026

View 15 scanner checks

live_secretremote_code_executionreverse_shelldata_exfiltrationssrf_metadataagent_snoopinganti_refusaldestructive_commandsobfuscated_unicodeunicode_homoglyphopaque_blobsuspicious_urltool_overreachtrigger_abuseprompt_injection_phrasing

IntentSafe

LLM judge · does the skill do what it claims

ContentClean

LLM judge · policy & harmful-content review

Source

Imported

vibeeval / vibecosystem

skills/math/complex-analysis/contour-integrals/SKILL.md

View on GitHub ↗

License MITImported 8/1/2026Version v1

Other skills for the same job

Published skills whose descriptions closely match this one, with their headline benchmark lift.

vibeeval/residuesProblem-solving strategies for residues in complex analysisClose match+22 pp pass-rate lift

More skills from the same source and nearby in the registry, with their headline benchmark lift.

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See it in action

What's inside

Contour Integrals

When to Use

Decision Tree

Tool Commands

Sympy_Residue

Track record

Benchmark

Adoption

SkillSafety

Source

Other skills for the same job

Related skills