eigen

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

The description details output format (dict with eigenvalues and eigenvectors, complex numbers as pairs), which adds behavioral context beyond the bare function. However, it does not disclose limitations such as requiring a square matrix or potential numerical stability issues.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is short (2 sentences) and front-loaded with the purpose. It is efficient but could be slightly more structured (e.g., bullet points for output format).

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

For a simple mathematical tool with one parameter, the description covers basic output but lacks critical context like input constraints (matrix must be square) and return value interpretation (e.g., ordering of eigenvectors).

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

The input schema has 0% parameter description coverage, and the tool description adds no meaning beyond the schema's type definition. The parameter 'matrix' is not explained in terms of its expected shape or constraints.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Does the description clearly state what the tool does and how it differs from similar tools?

The description explicitly states 'compute eigenvalues and eigenvectors of a square matrix', providing a specific verb and resource. This clearly distinguishes it from sibling tools like 'determinant' or 'matrix_inverse'.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Does the description explain when to use this tool, when not to, or what alternatives exist?

No guidance on when to use this tool versus alternatives like 'determinant' or 'solve_linear_system'. Also no mention of prerequisites (e.g., matrix must be square).

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.