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

With no annotations, the description should fully disclose behavioral traits, but it only vaguely states 'structure' without specifying the return format (e.g., vector of cyclic components, group invariants). It does not mention that the tool is a read-only computation with no side effects.

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 a single sentence, which is concise, but it sacrifices necessary detail about what 'structure' entails. It is front-loaded with the action, but the brevity limits its helpfulness for an AI agent unfamiliar with the notation.

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 presence of an output schema (not shown), the description may not need to explain return values. However, the concept of 'structure' is ambiguous and could benefit from additional context. For a single-parameter tool with high schema coverage, the description is minimally adequate but not fully informative.

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 describes 'n' as 'Positive integer,' and the description adds context by clarifying that n is the modulus for the multiplicative group (Z/nZ)*. This enhances meaning beyond the schema, which only labels the type.

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 specific mathematical computation: 'Compute the structure of (Z/nZ)*'. This distinguishes it from sibling tools like znorder or znlog which operate on elements within the group. The verb 'compute' and resource 'structure of (Z/nZ)*' are precise.

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 such as znorder, znlog, or other group theory tools. There is no mention of prerequisites, constraints, or contextual cues that would help an agent decide to invoke this tool.

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