apply_mobius_inversion

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. It mentions applying Möbius inversion but doesn't describe what the tool returns, whether it's a read-only computation or has side effects, error conditions, or performance characteristics. For a mathematical tool with three parameters, 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 very concise—a single sentence plus domain/category tags. It's front-loaded with the core action and wastes no words. However, this conciseness comes at the cost of completeness, as it omits necessary details about parameters and usage.

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 three undocumented parameters, no annotations, and no output schema, the description is inadequate. It doesn't explain what the tool returns, how to interpret results, or provide examples. The agent would struggle to use this tool correctly without additional context or experimentation.

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%, meaning none of the three parameters ('formula', 'n', 'description') are documented in the schema. The description only vaguely references 'a function defined by a formula' without explaining what the formula format should be, what 'n' represents, or how the optional 'description' parameter is used. This 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 'Apply Möbius inversion to a function defined by a formula' which provides a clear verb ('Apply Möbius inversion') and resource ('function defined by a formula'), but it's somewhat vague about what constitutes a 'formula' and doesn't distinguish from siblings like 'mobius_function' or 'mobius_inversion_formula'. The domain/category tags add context but don't fully clarify the specific 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?

No guidance is provided on when to use this tool versus alternatives. The description doesn't mention prerequisites, typical use cases, or how it differs from related tools like 'mobius_function' or 'mobius_inversion_formula'. The agent must infer usage from the tool name alone.

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