combinations

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

With no annotations, the description carries the full burden of behavioral disclosure. It usefully reveals that computation is exact and arbitrary-precision, which is meaningful. However, it omits edge-case behavior, such as what happens when r > n, and does not describe the return format.

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 with no filler. It front-loads the operation, names the mathematical concept, and adds the key precision guarantee in a compact way.

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?

This is a simple two-parameter pure function, so the description plus schema is mostly sufficient. However, there is no output schema to clarify return value format, and common edge cases such as r > n are not mentioned. It is adequate but not fully complete.

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. The nCr notation implies that n is the total and r is the selection size, but the description does not explain parameter roles explicitly or mention constraints beyond the schema's minimums. Some meaning is added, but it is minimal.

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 operation ('Compute nCr') and the resource ('combinations'), and the mathematical notation makes the tool's purpose unambiguous. It does not explicitly differentiate from sibling tools like permutations, but the 'combinations' keyword provides strong disambiguation.

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 explicit when-to-use guidance or exclusion of alternatives is provided. However, the phrase 'nCr (combinations)' implies usage when computing combinations, and 'exactly using arbitrary-precision integer math' suggests suitability for large values where floating-point approximations could be an issue.

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