solve_pell_equation

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

With no annotations provided, the description carries the full burden of behavioral disclosure. It states what the tool does but doesn't describe any behavioral traits: no information about computational complexity, error handling, input constraints (e.g., n must be non-square), output format, or performance characteristics. This is inadequate for a mathematical solver tool.

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 very concise - a single sentence plus domain/category tags. It's front-loaded with the core purpose and wastes no words. However, the extreme brevity comes at the cost of completeness, as noted in other dimensions.

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?

For a mathematical solver with no annotations, no output schema, and 0% schema description coverage, the description is incomplete. It doesn't explain what a 'fundamental solution' means, what format the output takes, any limitations or constraints, or how it relates to other Pell equation tools in the system. The context signals indicate this tool needs much more documentation.

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 0% description coverage, with only one parameter 'n' of type integer. The description mentions 'n' in the equation context but provides no additional semantic information: no constraints (e.g., n must be positive, non-square), no examples, no explanation of what 'n' represents mathematically. This leaves significant gaps in parameter understanding.

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 for fundamental solution.' It specifies the mathematical equation, the type of solution (fundamental), and includes domain/category context. However, it doesn't explicitly differentiate from sibling tools like 'cf_solve_pell' or 'solve_negative_pell_equation', which would be needed for 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 no guidance on when to use this tool versus alternatives. While it mentions the domain (arithmetic) and category (diophantine_equations), it doesn't specify use cases, prerequisites, or compare it to related tools like 'cf_solve_pell' or 'solve_negative_pell_equation' that appear in the sibling list.

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