frontiermath_number_theory

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

With no annotations, the description carries the full burden of disclosing behavior. It only states that computations are performed, omitting details about return format, side effects, or safety. For a pure computation tool, it does not confirm whether it is read-only or mention any prerequisites.

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 concise sentence, front-loaded with the verb 'Perform' and only includes essential clarifying examples. Every word earns its place, with no redundancy or fluff.

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?

The tool has no output schema and no annotations, so the description should explain return values and any constraints. It does not mention what the computation returns, how results are formatted, or any limitations on primeLimit. This leaves significant gaps for the agent.

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 coverage is 100%, so the baseline is 3. The description adds context by naming the specific computation types (multiplicative orders, density) that map to the operation parameter, but it does not clarify primeLimit beyond its schema description. Thus, it provides modest added meaning.

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 tool performs number theory computations, with specific examples (multiplicative orders, density calculations) that give concrete meaning. It distinguishes from sibling tools by naming a distinct mathematical subfield, though 'computations' remains somewhat broad.

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 for when to use this tool versus alternatives. The description does not mention any exclusions or reference sibling tools, leaving the agent to infer usage solely from the tool name and general description.

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