mertens_function_sieve

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 method ('using sieve') but doesn't disclose computational complexity, performance characteristics, error handling, or output format. For a mathematical computation tool with no annotations, this leaves significant behavioral gaps.

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: the first sentence states the core purpose clearly. The parenthetical domain/category adds context without verbosity. No unnecessary words, though it could be slightly more informative given the lack of annotations.

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 low schema coverage, the description is incomplete. It doesn't explain what the output looks like (e.g., integer result), error conditions, or practical usage notes. For a computational tool, this leaves the agent with insufficient context to use it effectively.

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 description must compensate. It defines n as the upper limit in the summation (k=1 to n), which adds essential meaning beyond the schema's type declaration. However, it doesn't specify constraints (e.g., n must be positive integer) or provide examples, leaving some ambiguity.

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 Mertens function M(n) = Σμ(k) for k=1 to n using sieve.' It specifies the mathematical function, the method (sieve), and the parameter n. However, it doesn't explicitly differentiate from sibling tools like 'mobius_function' or 'mobius_function_range' which might be related.

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 minimal guidance: it mentions the domain (arithmetic) and category (sieve_algorithms), but offers no explicit advice on when to use this tool versus alternatives like 'mobius_function_range' or other number theory tools. No prerequisites, limitations, or comparison to siblings are included.

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