eulerPhi

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

No annotations are provided, so the description carries the full burden. While it explains what the function computes, it doesn't disclose behavioral traits such as input validation (e.g., handling of non-positive integers, large values), performance characteristics, error handling, or output format. For a mathematical tool with no annotation coverage, this leaves significant gaps in understanding how the tool behaves.

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, efficient sentence that directly states the tool's purpose without any wasted words. It is appropriately sized and front-loaded, making it easy to understand at a glance.

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 of a mathematical function with no annotations, no output schema, and low parameter documentation, the description is incomplete. It lacks information on output format, error conditions, performance, and practical usage examples, which are important for an AI agent to invoke the tool correctly in varied contexts.

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%, but the description adds meaning by explaining that 'n' is the input for Euler's totient function. However, it doesn't provide details beyond the basic definition, such as valid ranges (though the schema specifies -2147483648 to 2147483647) or handling of edge cases. With one parameter and low schema coverage, the description compensates partially 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 specific mathematical function (Euler's totient function φ(n)) and defines it precisely as 'the number of positive integers less than or equal to n that are coprime to n.' It uses a specific verb ('计算' meaning 'calculate') with the resource (φ(n)), and distinguishes itself from sibling tools by focusing on this unique number theory function.

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 implies usage for computing Euler's totient function, which is sufficient given the mathematical context and sibling tools being distinct mathematical operations. However, it doesn't provide explicit guidance on when to use this versus alternatives (e.g., for primality testing or other number theory functions), nor does it mention any prerequisites or exclusions.

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