liouville_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. It states the function definition but does not disclose behavioral traits such as input constraints (e.g., n must be a positive integer), error handling, performance characteristics, or output format. This leaves significant gaps for an agent to understand how to invoke it correctly.

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 concise and front-loaded with the core function definition in a single sentence, followed by domain and category. There is no wasted text, making it efficient, though it could benefit from slightly more detail to improve usability.

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 function tool with no annotations, 0% schema coverage, and no output schema, the description is incomplete. It defines the function but lacks essential context such as parameter explanations, usage examples, error conditions, and output details, making it insufficient for reliable agent use.

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 does not add any parameter semantics. It mentions 'n' in the function but does not explain its meaning, constraints (e.g., must be a positive integer), or examples. With one undocumented parameter, the description fails to compensate for the lack of schema details.

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 with a specific mathematical function: 'Calculate the Liouville function λ(n) = (-1)^Ω(n).' It includes the domain (arithmetic) and category (arithmetic_functions), which distinguishes it from siblings like 'mobius_function' or 'big_omega' by specifying the exact formula and context.

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 does not specify use cases, prerequisites, or comparisons to sibling tools like 'mobius_function' or 'big_omega', which are related arithmetic functions.

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