solve_negative_pell_equation

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 tool solves the equation but does not disclose behavioral traits such as output format (e.g., integer solutions, existence check), computational complexity, or error handling for invalid inputs (e.g., n values with no solution). This is inadequate for a tool with mathematical operations.

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, stating the core purpose in one sentence with additional domain/category context. There is no wasted text, though it could be more informative without sacrificing brevity.

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 no annotations, no output schema, and low parameter coverage, the description is incomplete. It lacks details on behavior, output, and usage context, which are critical for a mathematical solving tool. The domain/category hints are insufficient for full understanding.

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 1 parameter (n) with 0% description coverage, so the description must compensate. It mentions 'n' in the equation but does not explain its semantics (e.g., integer constraints, typical range). This adds minimal value beyond the schema, meeting the baseline for low coverage.

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: solving the negative Pell's equation x² - ny² = -1. It specifies the mathematical domain (arithmetic) and category (diophantine_equations), making the verb+resource explicit. However, it does not differentiate from sibling tools like 'solve_pell_equation' (which likely solves x² - ny² = 1), missing full sibling distinction.

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. The description mentions the equation but does not specify prerequisites, constraints (e.g., valid n values), or refer to sibling tools like 'solve_pell_equation' for comparison. This leaves the agent without usage context.

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