von_mangoldt_function

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 calculates, without describing how it behaves: no information on input validation (e.g., n must be positive integer), computational characteristics (e.g., efficiency for large n), error handling, or output format. For a mathematical function tool with zero annotation coverage, this 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—a single sentence with domain/category tags. It's front-loaded with the core purpose and wastes no words. Every part earns its place, making it easy to parse quickly.

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 specialized mathematical function), lack of annotations, no output schema, and minimal parameter documentation, the description is incomplete. It doesn't explain the function's definition, typical use cases, output values (e.g., log(p) for prime powers, 0 otherwise), or mathematical context. For users unfamiliar with the von Mangoldt function, this description is insufficient.

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 a single parameter 'n' of type integer. The description doesn't add any parameter semantics beyond the schema—it doesn't explain what 'n' represents (e.g., a positive integer, the input to the von Mangoldt function) or any constraints. With no schema descriptions, the baseline is low, but the description fails to compensate, leaving the parameter meaning 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: 'Calculate the von Mangoldt function Λ(n).' It specifies the verb ('calculate') and the mathematical function, and provides domain/category context ('Domain: arithmetic, Category: arithmetic_functions'). However, it doesn't explicitly differentiate from sibling tools like 'liouville_function' or 'mobius_function', which are also 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. It mentions the domain and category, but doesn't explain what the von Mangoldt function is used for (e.g., prime number theory, analytic number theory) or when it's appropriate compared to other arithmetic functions in the sibling list. There's no mention of prerequisites, typical use cases, or limitations.

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