is_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 only states what the tool does ('Check if a number is an s-gonal number') without describing how it performs the check, what it returns (e.g., boolean, details), error handling, or performance considerations. This leaves significant gaps in understanding the tool's behavior.

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—a single sentence with a parenthetical domain/category. It is front-loaded with the core purpose and wastes no words. Every part of the description earns its place by adding context without redundancy.

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 complexity (a mathematical check with two parameters), lack of annotations, 0% schema coverage, and no output schema, the description is incomplete. It does not explain the mathematical definition of an s-gonal number, parameter roles, return type, or edge cases. The domain/category hint is insufficient to make the tool fully understandable.

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% description coverage, with parameters 'num' and 's' undocumented. The description does not explain what these parameters mean (e.g., 'num' is the integer to test, 's' is the number of sides/polygon type) or their constraints (e.g., s >= 3). It fails to compensate for the lack of schema documentation, leaving parameters semantically unclear.

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: 'Check if a number is an s-gonal number.' It specifies the verb ('Check') and resource ('s-gonal number'), and includes a domain/category for context. However, it does not explicitly differentiate from sibling tools like 'is_triangular_number' or 'is_pentagonal_number', which are specific cases of polygonal numbers.

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 does not mention sibling tools like 'is_triangular_number' (for s=3) or 'is_pentagonal_number' (for s=5), nor does it explain when to prefer this general tool over specific ones. The domain/category hint is minimal and does not constitute actionable usage advice.

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