Verify lattice conventions and bilinear form relations with exact arithmetic.
npx skills add https://github.com/dzackgarza/ai --skill lattices
Please help me install this Agent Skill. Skill: lattices Source: https://github.com/dzackgarza/ai/tree/main/opencode/skills/lattices Command: npx skills add https://github.com/dzackgarza/ai --skill lattices
Clarifies and standardizes mathematical conventions for lattices, bilinear forms, Gram and Cartan matrices, and related invariants to aid researchers in reasoning, communicating, and implementing computations.
Provide a lattice basis and request a formal verification of the associated Gram and Cartan conventions.
High-intent search queries and answers about installing and using this skill.
Verify Gram matrix conventions by providing a lattice basis to check B(v,v) definiteness and transformation relations. The Skill automates this verification using exact arithmetic over Z and Q.
The difference between a Gram matrix and a Cartan matrix lies in their associated bilinear form conventions. The Skill establishes precise terminology to distinguish these constructs and standardizes their relationships for mathematical research.
Validate lattice basis transformations in SageMath by applying exact arithmetic over Z and Q. The Skill guides safe implementation practices and checks transformation relations between Gram and Cartan matrices.
Yes, you can use exact arithmetic over minimal fields for bilinear form computations. The Skill requires reasoning with exact arithmetic over Z, Q, and minimal fields to verify lattice and bilinear form relations accurately.
Standardize bilinear form terminology for mathematical implementation when communicating or reasoning about lattice invariants. The Skill clarifies conventions for bilinear forms versus inner products to aid researchers in precise computation.
Verifying lattice conventions without exact arithmetic risks numerical instability and incorrect bilinear form relations. The Skill enforces exact arithmetic over Z and Q to ensure safe implementation and mathematically rigorous results.
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