little_omega

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

No annotations are provided, so the description carries full burden. It states the calculation but doesn't disclose behavioral traits like input constraints (e.g., n must be positive integer, handling of edge cases like n=0 or 1), performance characteristics, or error handling. The description is minimal beyond the core 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 extremely concise—a single sentence that directly states the tool's purpose and includes domain/category tags. Every word earns its place with zero redundancy, and the information is front-loaded.

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 tool's low complexity (single integer input, arithmetic function) and no annotations or output schema, the description is minimally complete. It defines the function but lacks details on input constraints, output format, or error cases. For a simple calculator tool, this is adequate but leaves gaps.

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 (parameter 'n' is undocumented in schema), but the description implicitly defines 'n' as the input integer for ω(n). It adds essential semantic meaning by linking 'n' to the arithmetic function, though it doesn't specify constraints like n>0. With one parameter and no schema documentation, this provides adequate compensation.

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 explicitly states the verb 'calculate' and the specific arithmetic function ω(n) with its mathematical definition 'number of distinct prime factors', clearly distinguishing it from sibling tools like 'big_omega' (total prime factors) or 'prime_factors' (list of factors). It also includes domain/category context.

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 alternatives like 'big_omega' (which counts total prime factors with multiplicity) or 'prime_factors' (which lists prime factors). The description only states what it calculates without comparative context.

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