isPerfectNumber

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. While it explains what a perfect number is, it doesn't describe the tool's behavior: whether it returns a boolean, what happens with invalid inputs (e.g., negative numbers or non-integers given the schema allows negative integers), performance characteristics, or error handling. The description adds minimal behavioral context beyond the basic mathematical definition.

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 perfectly concise and front-loaded: a single sentence that directly states the tool's purpose with zero wasted words. Every element ('判断', '正整数', '完全数', '真因子之和') earns its place by contributing essential information about what the tool does.

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 tool's mathematical nature, no annotations, 0% schema coverage, and no output schema, the description is incomplete. It doesn't explain the return type (presumably boolean but unspecified), doesn't address input validation issues (schema allows negatives but description says positive integers), and provides no context about performance or limitations for large numbers. For a tool with one parameter but poor schema documentation, the description should do more to compensate.

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%, so the description must compensate for undocumented parameters. The description mentions '正整数' (positive integer) which adds semantic meaning beyond the schema's generic integer type with wide range (-2147483648 to 2147483647). However, it doesn't fully explain the parameter's purpose or constraints (e.g., that n should be positive despite the schema allowing negatives), leaving significant gaps in parameter understanding.

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's purpose: '判断一个正整数是否为完全数（等于其所有真因子之和）' which translates to 'determines whether a positive integer is a perfect number (equal to the sum of all its proper divisors)'. It specifies the verb ('判断' - determine), resource ('正整数' - positive integer), and distinguishes it from siblings by focusing on perfect number checking, unlike other mathematical functions like isPrime or divisorCount.

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. It doesn't mention sibling tools like isPrime, divisorCount, or divisorList that might be relevant for related number theory tasks. There's no context about when perfect number checking is appropriate compared to other mathematical operations available on the server.

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