jordan_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 it's a calculation function, implying it's read-only and non-destructive, but doesn't explicitly confirm this or mention any constraints like input validation, error handling, computational complexity, or output format. For a mathematical function tool with zero annotation coverage, this leaves significant behavioral gaps.

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: it states the core purpose in the first clause, adds clarifying context in parentheses. There's zero wasted language, and every word earns its place. The structure is optimal for a simple mathematical function tool.

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 function with 2 parameters), lack of annotations, no output schema, and 0% schema description coverage, the description is incomplete. It doesn't explain what the function computes mathematically, parameter semantics, return values, or error conditions. While conciseness is good, it sacrifices necessary completeness for this 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?

The input schema has 2 parameters (n and k) with 0% description coverage in the schema. The tool description provides no information about what these parameters represent, their mathematical meaning, valid ranges (e.g., n > 0, k integer), or units. This leaves both parameters completely undocumented beyond their types, which is inadequate for a mathematical function.

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 Jordan's totient function J_k(n) - generalization of Euler's totient.' It specifies the verb ('calculate'), the mathematical function, and provides context about its relationship to Euler's totient. However, it doesn't explicitly differentiate from sibling tools like 'euler_totient' beyond mentioning it's a generalization.

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'), which gives some context, but offers no explicit guidance on when to use this tool versus alternatives like 'euler_totient' or other arithmetic functions. There's no mention of prerequisites, typical use cases, or comparison to siblings.

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