number_theory_operation

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

With no annotations, the description must carry the full burden of behavioral disclosure. It does not mention return types, side effects, or operation-specific behavior (e.g., is_prime returns a boolean, factor_integer returns a factorization). The description adds no transparency beyond the operation names.

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 line, front-loaded with the domain name. It is concise and avoids redundant phrasing, but it slightly under-specifies by merely listing operations without context. Still, it earns its place given schema coverage.

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 handles five distinct operations with differing inputs and outputs. The description does not explain operation-specific behaviors or prerequisites, leaving significant gaps in context. The presence of an output schema mitigates return-value documentation, but the description still lacks essential guidance for a multi-operation tool.

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 100% (operation lists all values, a/b have descriptions). The description's enumeration of operations duplicates schema info but adds no extra meaning, such as which parameters are needed for which operation. Baseline 3 applies because the schema already documents parameters well.

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 identifies the tool as performing number theory operations and lists five specific operations (is_prime, factor_integer, next_prime, gcd, lcm), which distinguishes it from sibling tools like matrix_operation or differentiate_expression. The noun phrase lacks an explicit verb but the operation list provides clear scope.

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 given on when to use this tool versus alternatives. For example, it does not clarify when to use factor_integer here versus factor_expression in a sibling tool. The usage context is only implied by the domain name, not explicitly stated.

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