carmichael_lambda

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

No annotations are provided, so the description carries full burden. It mentions the mathematical definition but doesn't disclose behavioral traits: no information about input constraints (e.g., n must be positive integer), error handling, computational complexity, or output format. For a mathematical function tool with zero annotation coverage, this leaves significant gaps in understanding how the tool behaves operationally.

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 containing the core purpose and domain/category context. Every word earns its place with zero redundancy. The mathematical definition is stated efficiently without 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 no annotations, no output schema, and 0% schema description coverage for the single parameter, the description is incomplete. While concise, it doesn't compensate for the missing structured information. For a mathematical function tool, users need to know input constraints, output format, and mathematical context—none of which are adequately addressed.

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%, and the description provides no parameter information beyond the schema's 'n: integer'. It doesn't explain what 'n' represents mathematically (positive integer? any integer?), valid ranges, or special cases. With one undocumented parameter at 0% coverage, the description adds minimal value over the bare schema.

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 Carmichael function λ(n) - exponent of multiplicative group mod n.' It specifies the verb ('calculate'), the mathematical function (Carmichael function λ(n)), and provides domain/category context. However, it doesn't explicitly differentiate from sibling tools like 'euler_totient' or 'order_modulo' which are related arithmetic functions.

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 it mentions the domain ('arithmetic') and category ('arithmetic_functions'), it doesn't indicate typical use cases, prerequisites, or when one might choose this over similar functions like Euler's totient function. The agent must infer usage from the mathematical definition alone.

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