binomialCoefficient

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

With no annotations provided, the description carries full burden for behavioral disclosure but provides none. It doesn't mention whether the tool validates input constraints (like k ≤ n or non-negative integers), handles edge cases (like negative inputs), returns errors, or provides any information about the calculation method or performance characteristics.

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 extremely concise with just one sentence that directly states the tool's purpose. There's zero wasted text, and the information is front-loaded with no unnecessary elaboration.

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?

For a mathematical calculation tool with 2 parameters, 0% schema coverage, no annotations, and no output schema, the description is insufficient. It doesn't explain what the tool returns, how it handles edge cases, mathematical constraints, or error conditions. The context signals indicate this is a non-trivial mathematical operation that needs more explanation.

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?

The schema has 0% description coverage, so the description must compensate but provides minimal parameter semantics. It mentions 'n choose k' which implies n and k are the standard binomial coefficient parameters, but doesn't explain their mathematical meaning, valid ranges beyond the schema's technical limits, or what happens with invalid combinations (like k > n).

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 as '计算二项式系数 (n choose k)', which translates to 'calculate binomial coefficient (n choose k)'. This specifies the exact mathematical operation and identifies the two parameters (n and k). However, it doesn't explicitly differentiate from sibling tools like 'combination' which might serve a similar mathematical purpose.

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. There's no mention of when this tool is appropriate, what mathematical scenarios it applies to, or how it differs from related sibling tools like 'combination' or 'permutation' in the same server.

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