combination

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

No annotations are provided, so the description carries full burden. It states what the tool calculates but doesn't disclose important behavioral aspects: no information about input validation (e.g., what happens if r > n or if values are negative), no mention of computational limits or performance characteristics, and no description of error handling. The description is purely functional without behavioral 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 a single, efficient sentence in Chinese that directly states the tool's purpose with zero wasted words. It's appropriately sized for this simple mathematical function and front-loads the essential information immediately.

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, 0% schema description coverage, and no output schema, the description is incomplete. It explains what the tool calculates but doesn't cover: input constraints, error conditions, return format, mathematical domain restrictions, or performance considerations. For a mathematical tool with two parameters, more contextual information would be helpful for proper usage.

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 schema provides no parameter documentation. The description adds meaningful semantics by explaining that 'n' represents total elements and 'r' represents selected elements for the combination calculation. However, it doesn't specify constraints (e.g., r ≤ n, non-negative integers) or provide examples of valid values, leaving 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 specific mathematical operation: '计算从n个元素中选择r个元素的组合数 C(n,r)' which translates to 'calculate the number of combinations C(n,r) of selecting r elements from n elements'. It uses precise mathematical terminology and distinguishes itself from sibling tools like 'permutation' by specifying it's about combinations rather than permutations.

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 implies usage for combinatorial calculations but doesn't explicitly state when to use this tool versus alternatives. While the mathematical context is clear, there's no guidance about when to choose this over other mathematical tools or what specific scenarios warrant its use. The sibling tool list includes 'permutation' which is closely related, but no comparison is provided.

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