mobius_function

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

No annotations are provided, so the description carries full burden. It states what the tool does ('Calculate') but doesn't disclose behavioral traits like input constraints (e.g., n must be positive integer), computational characteristics, error handling, or output format. For a mathematical function tool with zero annotation coverage, this leaves significant gaps in understanding how it behaves.

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 with zero wasted words. The first sentence directly states the purpose, and the parenthetical adds domain context efficiently. Every element 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 no annotations, 0% schema coverage, and no output schema, the description is incomplete. For a mathematical function tool, it should at minimum specify the parameter meaning and typical return values (e.g., returns -1, 0, or 1). The current description leaves too much undefined 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?

Schema description coverage is 0%, so the description must compensate. It mentions 'μ(n)' which implies a single integer parameter n, but doesn't explain what n represents (e.g., positive integer), valid ranges, or special cases (e.g., n=1 returns 1, n with squared prime factor returns 0). The description adds minimal semantic value beyond 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 Möbius function μ(n)' with specific verb ('Calculate') and resource ('Möbius function μ(n)'). It distinguishes from siblings by specifying the mathematical function, though it doesn't explicitly contrast with similar arithmetic tools like 'mobius_function_range' or 'liouville_function'.

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 includes domain/category tags ('Domain: arithmetic, Category: arithmetic_functions'), but these are generic and don't help differentiate from many sibling tools in the same categories. No explicit when/when-not instructions or named alternatives are provided.

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