stirling_numbers

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

No annotations are provided, so the description carries the full behavioral burden. It mentions the DP implementation, but does not disclose the return type, error behavior, determinism, or other behavioral traits; 'compute' implies a pure calculation but is not explicit.

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 a single front-loaded sentence with no wasted words. It delivers the essential purpose and method immediately.

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 deterministic math tool with complete schema descriptions and no output schema, the description is largely sufficient: it states what is computed and the implementation method. It could mention the return type or default kind, but those are minor given the schema.

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?

Schema description coverage is 100%, so the schema already documents n, k, and kind with ranges and defaults. The description adds no parameter meaning beyond what the schema provides, so the baseline of 3 is appropriate.

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 uses a specific verb ('Compute') and names the exact mathematical resource ('Stirling numbers of the first or second kind'). It also distinguishes the two variants, so an agent can tell what the tool produces without opening the schema.

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?

The description implies usage by naming the computation, but it does not explicitly state when to use this tool versus alternatives or when not to use it. No sibling tools are named or contrasted, so usage guidance is only implied.

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