cf_solve_pell

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 solves Pell's equation using continued fractions, which implies a computational process, but doesn't describe what the tool actually returns (e.g., fundamental solution, all solutions, specific format), performance characteristics, error handling, or any constraints on the input 'n' (e.g., must be non-square). This leaves significant gaps in understanding the tool's 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 concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. The additional domain and category information in parentheses is brief and relevant. There's no wasted verbiage, making it efficient, though it could benefit from more detail given the complexity of the 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 of solving Pell's equation, the lack of annotations, no output schema, and minimal parameter semantics, the description is incomplete. It doesn't explain what the tool returns (e.g., a solution pair, a list of solutions), how solutions are represented, or any algorithmic details. For a mathematical tool with potential nuances, this leaves too much unspecified for effective 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 in the schema. The description doesn't add any semantic information about 'n'—it doesn't explain what 'n' represents in Pell's equation (e.g., a non-square integer), valid ranges, or constraints. This is inadequate given the low schema coverage, failing to compensate for the lack of parameter documentation.

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: 'Solve Pell's equation x² - ny² = 1 using continued fractions.' It specifies both the mathematical equation and the method (continued fractions), which is specific and informative. However, it doesn't explicitly differentiate from sibling tools like 'solve_pell_equation' or 'pell_solutions_generator' that might have overlapping functionality.

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 (continued_fractions), which gives some context, but offers no explicit guidance on when to use this tool versus alternatives like 'solve_pell_equation' or other Pell-related tools in the sibling list. There's no mention of prerequisites, limitations, or typical use cases.

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