sympy_binomial

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

With no annotations, the description must disclose behavioral traits, but it only states the mathematical concept. It does not mention that the tool returns a symbolic expression, any constraints on inputs beyond the schema, or side effects. The minimal description fails to inform about behavior.

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 (two words), but it is under-specified. It does not earn its place because it adds almost no value beyond the tool name and schema. A more informative but still concise description would be better.

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 simplicity of the tool and the presence of an output schema, the description is incomplete. It does not clarify the return type (symbolic expression vs. numeric), nor does it provide enough context given the large number of sibling tools. The description should at least mention that it computes the binomial coefficient symbolically.

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 100%, and the schema already describes both parameters as 'Non-negative integer'. The description adds no semantic meaning beyond this. Baseline of 3 is appropriate since the schema does the heavy lifting.

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 'Binomial coefficient' clearly states the mathematical operation. It is specific to the binomial coefficient function, distinguishing it from unrelated tools, but does not differentiate it from closely related combinatorial functions like factorial or Catalan numbers, which are also present as sibling tools.

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 usage guidance is provided. The description does not indicate when to use this tool versus alternatives such as sympy_factorial or sympy_catalan, nor does it mention any prerequisites or context for use.

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