Number Theory

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

Annotations are empty, so the description must disclose behavior. It says 'Number theory operations' but does not mention whether it is read-only, requires authentication, or how it handles errors. The safety profile is unclear.

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 short sentence, which is concise but lacks structure and essential details. It is under-specified rather than efficiently informative.

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 moderate complexity (2 params, many sibling tools), the description is incomplete. It does not explain outputs, differentiate from similar tools, or provide behavioral context, despite the output schema existing.

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% with clear parameter descriptions (number: 'Integer to analyze', operation: 'Number theory operation (is_prime, prime_factors, divisors, totient)'). The description adds no extra semantic value beyond the schema, earning a baseline score of 3.

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 'Number theory operations' is vague and does not specify a clear verb+resource. The title 'Number Theory' is equally generic. The schema shows operations like is_prime, prime_factors, divisors, totient, but the description omits these, making it unclear what the tool does.

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 on when to use this tool vs. alternatives like calculate_expression or calculate_statistics. The description provides no context for selection, leaving the agent without decision support.

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