primitive_root

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 only states what the tool does ('Find the smallest primitive root modulo n') but provides no information about error conditions (what happens if n has no primitive roots), computational characteristics, input constraints (must n be positive? prime?), or output format. This is inadequate for a tool with mathematical constraints.

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 extremely concise - a single sentence plus domain/category tags. It's front-loaded with the core functionality. However, the conciseness comes at the cost of completeness; while there's no wasted text, the description may be too brief for adequate tool understanding.

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 that there are no annotations, no output schema, and 0% schema description coverage for the single parameter, the description is insufficiently complete. A mathematical tool for finding primitive roots needs more context about input constraints, error handling, and output format. The description doesn't address these critical aspects, making it inadequate for reliable 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 the parameter 'n' is completely undocumented in the schema. The description mentions 'modulo n' which gives some context that n is the modulus, but doesn't explain what values are valid (must be integer > 1? prime? odd?), what happens with invalid inputs, or the mathematical meaning of 'primitive root modulo n'. This minimal information doesn't adequately 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 'Find the smallest primitive root modulo n' which clearly indicates the verb ('Find') and resource ('primitive root modulo n'). However, it doesn't differentiate from sibling tools like 'all_primitive_roots' which would return all primitive roots rather than just the smallest one. The domain/category tags are helpful but don't improve the core purpose statement.

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. There's no mention of when this tool is appropriate, what prerequisites might be needed (e.g., n must be a prime or have primitive roots), or when to choose other tools like 'all_primitive_roots' from the sibling list. The domain/category tags don't provide usage guidance.

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