is_deficient_number

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

No annotations are provided, so the description carries full burden. It mentions the mathematical operation but doesn't disclose behavioral traits like input validation (e.g., handling of non-positive integers), performance characteristics, error conditions, or return format. The description is purely functional without operational context.

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 efficiently structured in a single sentence that states the purpose and mathematical definition, with no wasted words. The domain/category in parentheses is slightly extraneous but not disruptive. It's appropriately front-loaded with the core functionality.

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 no annotations, no output schema, and minimal schema coverage, the description is incomplete. It doesn't explain what the tool returns (e.g., boolean, detailed analysis), error handling, or edge cases. For a mathematical function with potential input constraints, more context is needed.

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?

With 0% schema description coverage and only one parameter, the description adds value by implying 'n' should be an integer to check for deficiency. However, it doesn't specify constraints (e.g., positive integers only) or provide examples. The baseline is 3 since the schema covers the parameter type minimally.

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 specific verb ('Check if') and resource ('a number'), and defines the mathematical condition ('sum of proper divisors < n'). It distinguishes from siblings like 'is_abundant_number' and 'is_perfect_number' by specifying the deficiency condition.

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 like 'is_abundant_number' or 'is_perfect_number', nor does it mention prerequisites or typical use cases. The domain/category tags are generic and don't offer practical usage context.

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