euler_totient

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 states the tool calculates a mathematical function, implying it is a read-only, deterministic operation, but does not explicitly confirm this or mention any limitations (e.g., input constraints, performance considerations, or error handling). For a tool with no annotations, this leaves significant gaps in understanding its 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 and front-loaded: a single sentence that directly states the tool's purpose and includes domain/category tags. There is no wasted verbiage, and every element (function definition, domain) serves a clear purpose, making it efficient for an agent to parse.

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, no output schema, no annotations), the description is minimally adequate. It explains what the tool computes but lacks details on input validation, output format, or error cases. For a straightforward arithmetic function, this might suffice, but it does not provide a complete picture for reliable 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 one parameter 'n' with 0% description coverage. The description adds some semantic context by defining φ(n) as 'count of integers ≤ n coprime to n,' which clarifies the parameter's role. However, it does not specify constraints (e.g., n must be positive integer) or provide examples. Given the low schema coverage, the description partially compensates but not fully.

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 tool's purpose: 'Calculate Euler's totient function φ(n) - count of integers ≤ n coprime to n.' It specifies the verb ('calculate'), the mathematical function, and its definition. However, it does not explicitly differentiate from sibling tools like 'euler_totient_inversion' or other arithmetic functions, which prevents a perfect score.

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 minimal usage guidance: it mentions the domain ('arithmetic') and category ('arithmetic_functions'), but does not specify when to use this tool versus alternatives (e.g., 'euler_totient_inversion' or other number theory tools). No explicit when/when-not instructions or prerequisites are given, leaving the agent with little contextual direction.

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