euler_totient_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 the mathematical method (Möbius inversion) but doesn't describe what the tool returns (e.g., a single integer value, a formula, or an error for invalid inputs), computational complexity, or edge cases (e.g., handling of n ≤ 0). This leaves significant gaps in understanding how the tool behaves beyond its basic purpose.

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, stating the core purpose in a single sentence. The domain and category tags are included but don't add unnecessary verbosity. However, the lack of additional useful information (e.g., usage guidelines or parameter details) means it could be more informative without losing conciseness.

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 derivation tool with no annotations, no output schema, and poor parameter documentation, the description is incomplete. It doesn't explain the return value, error conditions, or how it differs from related tools. For a tool performing a non-trivial mathematical operation, this level of detail is inadequate for an agent 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?

The input schema has 0% description coverage, documenting only that 'n' is an integer. The description adds no information about parameter semantics—it doesn't explain what 'n' represents (e.g., a positive integer for which to compute the totient), valid ranges, or constraints. With low schema coverage, the description fails to compensate, leaving the parameter poorly defined.

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 'Derive Euler's totient function using Möbius inversion', which specifies the mathematical operation (derive) and the function (Euler's totient). However, it doesn't clearly distinguish this from sibling tools like 'euler_totient' (which likely computes the totient directly) or 'mobius_inversion_formula' (which likely performs the inversion generally). The domain/category tags add context but don't clarify the specific purpose relative to alternatives.

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 comparisons to sibling tools like 'euler_totient' or 'mobius_inversion_formula'. Without this, an agent must infer usage from the name and description alone, which is insufficient for informed tool selection.

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