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Fields · vibeeval | DecimalAI

scienceby vibeeval

Fields

vibeeval/fields

Source vibeeval/vibecosystem ↗License MIT

Problem-solving strategies for fields in abstract algebra

SkillScore91Maintained

Automatic

Tutoring & Education pack

Last verified 8/3/2026

What it changes

Passed 20 of 22 test cases with the skill, and 16 of 22 without it.

Without skill73%

With skill91%

Checks it passed that the model alone missed

Uses scripts/sympy_compute.py.
Passes "field_axioms" as the target parameter.
Invokes sympy_compute.py minpoly script to calculate the minimal polynomial.

and 1 more in the full report

4 fixed16 passed either way2 still failing0 broke

Pass-rate lift: +18 pp
Tokens: +26%
Agent turns: 0%
Response time: -31%

Model gemini-3.6-flashMeasured 8/3/2026v120 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-fields/SKILL.md https://app.decimal.ai/s/vibeeval-fields/SKILL.md

Want it pinned and updatable? pip install "decimalai>=0.15", then decimalai skills add vibeeval-fields, 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-fields/ and pins it in .decimal/skills.lock

decimalai skills add vibeeval-fields

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

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

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

Safety checks: 3 of 3 passed

Code scan CleanIntent PassedContent Clean

See it in action

One of 4 test cases the skill fixed. Same model, same prompt, with and without the skill.

1 of 4

Prompt

Which python script in the harness is designated for solving polynomial equations like p(alpha) = 0?

What was checked, without and with the skill
Checked	Without skill	With skill
Uses scripts/sympy_compute.py.	Missed	Passed

case-19 · 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.md60 linessingle file

Fields

When to Use

Use this skill when working on fields problems in abstract algebra.

Decision Tree

Is F a field?
- (F, +) is an abelian group with identity 0
- (F \ {0}, *) is an abelian group with identity 1
- Distributive law holds
- z3_solve.py prove "field_axioms"
Field Extensions
- E is extension of F if F is subfield of E
- Degree [E:F] = dimension of E as F-vector space
- sympy_compute.py minpoly "alpha" --var x for minimal polynomial
Characteristic
- char(F) = smallest n > 0 where n*1 = 0, or 0 if none exists
- char(F) is 0 or prime
- For finite field: |F| = p^n where p = char(F)
Algebraic Elements
- alpha is algebraic over F if it satisfies polynomial with coefficients in F
- sympy_compute.py solve "p(alpha) = 0" for algebraic relations

Tool Commands

Z3_Field_Axioms

uv run python -m runtime.harness scripts/z3_solve.py prove "field_axioms"

Sympy_Minpoly

uv run python -m runtime.harness scripts/sympy_compute.py minpoly "sqrt(2)" --var x

Track record

Benchmark

20 / 22

test cases passed, vs 16 / 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/abstract-algebra/fields/SKILL.md

View on GitHub ↗

License MITImported 8/1/2026Version v1

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

Fields

When to Use

Decision Tree

Tool Commands

Z3_Field_Axioms

Sympy_Minpoly

Track record

Benchmark

Adoption

SkillSafety

Source

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