pentagonal_number

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

No annotations are provided, so the description carries the full burden. It states the calculation formula but does not disclose behavioral traits such as input validation (e.g., handling negative integers), error handling, performance characteristics, or output format. This leaves gaps in understanding how the tool behaves beyond the basic computation.

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 highly concise and front-loaded, consisting of a single sentence that directly states the tool's function and formula, followed by domain/category tags. Every element earns its place without redundancy or unnecessary elaboration.

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?

Given the tool's low complexity (single integer parameter, no output schema, no annotations), the description is adequate for basic use but incomplete. It lacks details on output format, error handling, and behavioral context, which are important for a tool with no structured annotations to guide the agent.

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 1 parameter with 0% description coverage, but the description compensates by defining 'n' in the formula context: 'nth pentagonal number P_n = n(3n-1)/2.' This clarifies that 'n' is an integer index for the pentagonal number, adding meaningful semantics beyond the schema's type declaration.

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 the tool's purpose: 'Calculate the nth pentagonal number P_n = n(3n-1)/2.' It includes the specific verb 'calculate,' the resource 'pentagonal number,' and the exact mathematical formula, which clearly distinguishes it from siblings like 'is_pentagonal_number' or 'pentagonal_sequence' that serve different purposes.

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 through the formula and domain/category tags ('arithmetic, basic_sequences'), suggesting it's for computing pentagonal numbers in mathematical contexts. However, it lacks explicit guidance on when to use this tool versus alternatives like 'pentagonal_sequence' or 'is_pentagonal_number,' and does not mention any prerequisites or exclusions.

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