bell_number

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

No annotations are provided, so the description carries full burden for behavioral disclosure. It only states what the tool calculates, without mentioning computational characteristics (e.g., performance with large n, precision limits, error handling for invalid inputs, or return format). For a mathematical computation tool with zero annotation coverage, this leaves significant behavioral gaps.

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 extremely concise and front-loaded: the first phrase states the core functionality, followed by the mathematical definition in parentheses, and ends with domain/category tags. Every element adds value with zero wasted words, making it easy for an agent to parse quickly.

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 single-parameter mathematical tool with no annotations and no output schema, the description provides adequate basic purpose and parameter semantics. However, it lacks information about return values (what format the Bell number is returned in), error conditions, computational limits, or relationships to sibling tools. The completeness is minimal but acceptable for this simple function.

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?

With 0% schema description coverage for the single parameter 'n', the description compensates by explaining that 'n' represents the index for the Bell number calculation ('the nth Bell number'). This adds essential semantic meaning beyond the schema's type declaration. However, it doesn't specify constraints like valid ranges or integer requirements beyond what's implied.

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 clearly states the tool's purpose: 'Calculate the nth Bell number B_n' with the specific mathematical definition 'number of partitions of a set'. It distinguishes this tool from siblings like 'bell_sequence' and 'bell_triangle' by focusing on individual Bell number calculation rather than sequences or triangles. The domain/category tags further clarify the mathematical context.

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 provides no guidance on when to use this tool versus alternatives. While it mentions the mathematical domain, it doesn't indicate when to choose this over similar combinatorial tools (like 'partition_count' or 'distinct_partitions'), nor does it specify any prerequisites, limitations, or typical use cases for Bell number calculations.

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