all_primitive_roots

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 tool 'finds' primitive roots, implying a read-only operation, but does not specify output format (e.g., list of integers), computational complexity, or error handling for invalid inputs (e.g., when 'n' has no primitive roots). For a tool with no annotations, this leaves significant behavioral gaps.

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 stated in the first sentence. The domain/category tags are brief and relevant. There is no wasted verbiage, making it efficient, though it could benefit from additional clarifying details.

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 modular arithmetic, no annotations, no output schema, and low parameter schema coverage, the description is incomplete. It does not explain what primitive roots are, the return values, or edge cases, which are essential for an AI agent to use the tool correctly in this mathematical context.

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, with one parameter 'n' of type integer. The description does not add any semantic information about 'n', such as its meaning (modulus), constraints (e.g., must be positive integer > 1), or examples. With low schema coverage, the description fails to compensate, leaving the parameter poorly documented.

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's purpose ('Find all primitive roots modulo n') with a specific verb ('Find') and resource ('primitive roots modulo n'), which is clear. However, it does not distinguish this tool from its sibling 'primitive_root' (singular), leaving ambiguity about whether this tool returns all roots versus a single root. The domain/category tags add context but don't clarify this distinction.

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. It does not mention the sibling tool 'primitive_root', nor does it specify conditions like when 'n' must be prime or have primitive roots, or any prerequisites for usage. The agent is left without explicit usage instructions.

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