partitions_into_k_parts

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

No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions the mathematical domain and category, but does not describe computational behavior such as performance characteristics (e.g., for large n/k), error handling, or output format. The description is minimal and lacks details on what the tool returns or how it operates beyond the basic purpose.

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 very concise—a single sentence plus domain/category tags—with no wasted words. It is front-loaded with the core purpose. However, it is arguably too brief, lacking necessary details for a tool with no annotations and low schema coverage, which slightly reduces its effectiveness despite the efficiency.

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 complexity (mathematical partition counting), lack of annotations, 0% schema description coverage, and no output schema, the description is incomplete. It does not explain the output (e.g., integer count, possible errors), parameter constraints, or behavioral traits. The domain/category tags add some context but are insufficient for a tool that requires more detailed guidance for correct use.

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 input schema has 0% description coverage, so the description must compensate. It explains that n and k are integers used for counting partitions, but does not specify their meaning (e.g., n is the integer to partition, k is the maximum number of parts), valid ranges (e.g., non-negative), or constraints (e.g., k ≤ n). This leaves significant gaps in understanding parameter semantics beyond basic types.

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 states the tool's purpose ('Count partitions of n into at most k parts'), which is clear but somewhat vague. It specifies the mathematical operation (counting partitions) and the parameters (n, k), but does not differentiate from sibling tools like 'distinct_partitions' or 'restricted_partitions' that also deal with partitions. The domain/category tags are helpful but not part of the core purpose statement.

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. It does not mention sibling tools like 'distinct_partitions' or 'restricted_partitions', nor does it explain the difference between 'at most k parts' and other partition types. There is no context on typical use cases or constraints, leaving the agent to infer usage from the name and parameters alone.

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