polygonal_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 of behavioral disclosure. It states the tool calculates a value but does not describe any behavioral traits such as error handling (e.g., for invalid inputs), performance characteristics, or output format. For a computational tool with zero annotation coverage, this is a significant gap in transparency.

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: a single sentence that directly states the tool's purpose, followed by domain/category in parentheses. There is no wasted text, and every part earns its place by providing essential information efficiently.

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 computational nature, two required parameters with 0% schema coverage, no annotations, and no output schema, the description is incomplete. It lacks parameter explanations, behavioral context, and output details, making it insufficient for an agent to use the tool effectively without additional inference or trial-and-error.

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 schema description coverage is 0%, meaning parameters 'n' and 's' are undocumented in the schema. The description does not add any meaning beyond the tool name—it does not explain what 'n' and 's' represent (e.g., 'n' as the index, 's' as the number of sides). With two required parameters and no schema or description coverage, this is inadequate.

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 s-gonal (polygonal) number.' It specifies the verb ('calculate') and resource ('polygonal number'), and includes domain/category context. However, it does not explicitly differentiate from sibling tools like 'centered_polygonal_number' or 'polygonal_sequence', which are closely related, preventing a perfect score.

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. It mentions the domain and category but offers no explicit when-to-use, when-not-to-use, or alternative tool recommendations (e.g., compared to 'centered_polygonal_number' or 'polygonal_sequence' in the sibling list). This leaves the agent without contextual usage direction.

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