lucas_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 calculation action but does not describe error handling (e.g., for negative or large 'n'), computational limits, or output format. For a mathematical tool with potential edge cases, this lack of behavioral detail is a significant gap.

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 directly states the tool's purpose, followed by domain and category in parentheses. Every word contributes essential information without redundancy, making it highly efficient and well-structured.

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 of a mathematical calculation tool with no annotations, no output schema, and low parameter schema coverage, the description is incomplete. It lacks details on behavior, output format, error conditions, and usage context. While concise, it does not provide enough information for reliable tool invocation in varied scenarios.

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 one parameter 'n' of type integer. The description adds minimal semantic context by specifying 'nth' and 'L_n', implying 'n' is an index. However, it does not explain valid ranges, constraints, or examples. Given the low schema coverage, the description partially compensates but remains insufficient for full parameter understanding.

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 Lucas number L_n.' It specifies the verb ('Calculate'), resource ('nth Lucas number'), and mathematical notation ('L_n'), making the intent unambiguous. However, it does not explicitly differentiate from sibling tools like 'lucas_sequence' or 'lucas_u_v', which are related but distinct operations.

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 ('arithmetic') and category ('recursive_sequences'), which hints at context, but does not specify scenarios, prerequisites, or comparisons to siblings like 'fibonacci' or 'lucas_sequence'. This leaves the agent without explicit usage instructions.

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