combinatorics

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

No annotations are present, so the description should disclose behavior. It only states 'evaluate', which implies computation but does not mention safety, side effects, or any constraints. The agent cannot infer whether this tool is read-only or has side effects.

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 sentence, which is too brief for a tool with 4 parameters and an output schema. It sacrifices informativeness for brevity, making it under-specified.

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 number of parameters and the presence of an output schema, the description lacks details about return values and the meaning of input fields. The agent cannot confidently invoke the tool without additional context.

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% for the 4 parameters. The description does not explain what 'operation', 'n', 'k', or 'as_formula' mean, leaving the agent without guidance on how to fill these fields.

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 'Evaluate combinatorial number sequences and counting functions' gives a general sense but lacks specificity about which sequences or operations are supported. The input schema has an 'operation' parameter without enumerated values, making it unclear what operations are available.

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 guidance is provided on when to use this tool versus siblings like 'partitions' or other combinatorial functions. No when-not-to-use or alternative suggestions are given.

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