mobius_inversion_formula

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. The description mentions what the tool does but doesn't explain how it behaves: it doesn't describe the expected format of g_values, what happens when n is invalid, whether the operation is deterministic, or what kind of output to expect. For a tool with 2 parameters and no annotations, this is insufficient.

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 purpose in the first clause. The parenthetical domain/category information is efficiently appended. No unnecessary words or redundant information is present.

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 transformation tool with 2 parameters, no annotations, no output schema, and 0% schema description coverage, the description is incomplete. It doesn't explain parameter meanings, expected behavior, output format, or error conditions. The domain/category hints are helpful but insufficient for proper tool invocation.

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%, meaning neither parameter has descriptions in the schema. The tool description doesn't explain what g_values or n represent, their expected formats, or their roles in the Möbius inversion. With 2 undocumented parameters, the description fails to compensate for the schema's lack of 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 clearly states the tool's purpose: 'Apply Möbius inversion formula to recover function from its summatory function.' It specifies both the action (apply formula) and the mathematical context (arithmetic domain, Möbius functions category). However, it doesn't explicitly differentiate from its sibling 'apply_mobius_inversion' tool, which appears to serve a similar purpose.

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 usage guidance. While it mentions the domain (arithmetic) and category (mobius_functions), it doesn't explain when to use this tool versus alternatives like 'apply_mobius_inversion' or other mathematical tools. No explicit when/when-not instructions or prerequisite conditions are provided.

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