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FrankieeWFrankieeW/agent-skills/lmfdb-cli/SKILL.md

lmfdb-cli

Skill0 starsChanged 8 months agoMITView on GitHub

Query LMFDB to verify number theory results, including number field properties, elliptic curve data, and algebraic number theory computations.

  • Installs packages

The file

We split this skill into the rules it gives an agent

3 rules. About 0 are common, 0 are distinctive, and 3 are very specific to this project.

  • ≈0

    Common · estimate

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  • ≈0

    Distinctive · estimate

    This author's own choices. Worth a look.

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  • Common
  • Distinctive
  • Very specific
  1. Very specific:

    Use lmfdb CLI to look up concrete examples and verify results against the LMFDB database.

    line 8
  2. Very specific:

    JSON for parsing: Use --fmt json when you need to process results programmatically.

    line 147
  3. Very specific:

    Specific fields: Use -f to request only the fields you need — makes output cleaner and queries faster.

    line 149

≈ “Common” is an estimate: at least 1 in 5 of the 350,495 skill files we read have a rule of the same kind, not the same words. “Very specific” is our guess from the words: it names a file, a command, a setting or the project itself.

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Files
SKILL.md

Querying LMFDB for Mathematical Verification

Use lmfdb CLI to look up concrete examples and verify results against the LMFDB database.

Installation

brew tap frankieew/tap && brew install lmfdb-cli
# or build from source: go build -o lmfdb ./cmd/lmfdb

Number Fields (nf)

Quick Reference

lmfdb nf [options]
FlagMeaningExample
-d <n>Degree [Q(α):Q]-d 3 (cubic fields)
-n <n>Number of results-n 50
--disc <val>Discriminant--disc -23
--class <n>Class number h(K)--class 1
--sig <r1,r2>Signature (r₁,r₂)--sig 0,1 (totally imaginary)
--id <label>Specific field by LMFDB label--id 2.0.3.1
--sort <field>Sort (prefix - for desc)--sort -disc
-f <fields>Select specific fields-f label,disc,class_number
--fmt jsonOutput as JSON--fmt json
-o <file>Save to file-o results.csv --fmt csv
--browserBypass reCAPTCHAfor large queries

Common Verification Tasks

Find all quadratic fields with class number 1:

lmfdb nf -d 2 --class 1 -n 100

Check imaginary quadratic fields (signature (0,1)):

lmfdb nf -d 2 --sig 0,1 -n 50

Look up a specific number field by label:

lmfdb nf --id 2.0.3.1
# Returns full record: discriminant, class number, Galois group, regulator, etc.

Cubic fields sorted by discriminant:

lmfdb nf -d 3 --sort disc -n 20

Totally real quartic fields:

lmfdb nf -d 4 --sig 4,0 -n 20

Export for further analysis:

lmfdb nf -d 2 -n 200 -f label,disc,class_number,regulator --fmt json -o quadratic_fields.json

LMFDB Number Field Labels

Format: d.r.D.n where:

  • d = degree
  • r = number of real embeddings (0 or positive)
  • D = absolute discriminant
  • n = index among fields with same (d, r, D)

Example: 2.0.3.1 = degree 2, no real embeddings, |disc| = 3, first such field = Q(√-3)

Available Fields for -f

Key fields in nf_fields collection:

  • label — LMFDB label
  • degree — [K:Q]
  • disc — discriminant Δ_K
  • class_number — h(K)
  • class_group — structure of Cl(K)
  • signature — [r₁, r₂]
  • regulator — regulator R_K
  • galt — Galois group (transitive group label)
  • subfields — subfield labels
  • zk — integral basis
  • coeffs — minimal polynomial coefficients

Elliptic Curves (ec)

Quick Reference

lmfdb ec [options]
FlagMeaningExample
-r <n>Mordell-Weil rank-r 2
-t <n>Torsion order-t 7
--conductor <n>Conductor N--conductor 11
-n <n>Number of results-n 50
--sort <field>Sort--sort conductor
-f <fields>Select fields-f lmfdb_label,rank,conductor

Common Verification Tasks

Find rank 2 elliptic curves:

lmfdb ec -r 2 -n 20

Curves with torsion group of order 7:

lmfdb ec -t 7 -n 10

Curves of conductor 11:

lmfdb ec --conductor 11 --fmt json

Export rank data for analysis:

lmfdb ec -r 0 -n 100 -f lmfdb_label,conductor,torsion_structure --fmt csv -o rank0_curves.csv

Other Collections

lmfdb list   # Show all available collections

Available: number fields, elliptic curves, genus 2 curves, Dirichlet characters, Maass forms, modular forms, local fields, Artin representations, Belyi maps.

Tips

  • reCAPTCHA blocking: For large queries (n > 50), use --browser flag. Run lmfdb install-browser first to download Chromium.
  • JSON for parsing: Use --fmt json when you need to process results programmatically.
  • Pagination: Combine -n and --offset to page through large result sets.
  • Specific fields: Use -f to request only the fields you need — makes output cleaner and queries faster.

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