centered_polygonal_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. The description only states what is calculated, with no information about input constraints (e.g., valid ranges for n and s), error conditions, computational characteristics, or output format. This leaves significant behavioral aspects undocumented.

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 with zero wasted words. The single sentence directly states the calculation purpose, and the parenthetical domain/category adds useful context without verbosity. This is appropriately front-loaded and efficient.

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 no annotations, 0% schema coverage, and no output schema, the description is incomplete. While concise, it fails to address key contextual elements: parameter meanings/constraints, behavioral characteristics, output format, or differentiation from related tools. For a mathematical calculation tool with two parameters, this leaves too many gaps.

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 0%, so the schema provides no parameter documentation. The description mentions 'nth' and 's-gonal' which correspond to the n and s parameters, but doesn't explain what these parameters represent (e.g., n is position/index, s is number of sides/polygon type) or any constraints (e.g., must be positive integers). This adds minimal semantic value beyond parameter names.

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 centered s-gonal number.' It specifies the verb ('calculate') and resource ('centered s-gonal number'), and includes domain/category context. However, it doesn't explicitly differentiate from sibling tools like 'centered_hexagonal_number' or 'polygonal_number', which are related figurate number calculations.

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 the domain/category hint ('figurate_numbers') suggests a mathematical context, there's no explicit mention of when this specific centered polygonal calculation is appropriate compared to regular polygonal numbers or other centered figurate tools in the sibling list.

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