divisor_function_inversion

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 domain (arithmetic) and category (mobius_functions) but doesn't disclose behavioral traits like what the tool returns (values, formulas, or analysis results), computational complexity, error conditions, or whether it performs read-only analysis versus mutation. The description is too vague about the actual behavior.

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 with two brief clauses, though the parenthetical domain/category information could be considered redundant if available elsewhere. It's front-loaded with the core purpose, but could be more informative without sacrificing brevity.

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?

For a mathematical tool with 3 parameters, no annotations, no output schema, and 0% schema coverage, the description is inadequate. It doesn't explain what the tool returns, how parameters interact, or provide examples of typical use cases. The domain/category tags don't compensate for the missing operational details.

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?

With 0% schema description coverage for 3 parameters, the description provides no information about parameters. It doesn't explain what 'n', 'function_type', or 'power' represent, their valid ranges, or how they affect the analysis. The description fails to compensate for the complete lack of schema documentation.

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 states the tool 'Analyze divisor functions using Möbius inversion techniques' which provides a general purpose (analyzing divisor functions) and method (Möbius inversion). However, it doesn't specify what kind of analysis is performed (e.g., computing values, verifying properties, or transforming functions) or distinguish it from sibling tools like 'divisor_count', 'divisor_sum', or 'mobius_inversion_formula'.

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. With many sibling tools related to divisors, Möbius functions, and arithmetic operations, there's no indication of when this specific inversion technique is appropriate versus other divisor analysis tools or the general 'mobius_inversion_formula' tool.

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