solve_quadratic_diophantine

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. The description mentions the equation form but doesn't explain key behavioral aspects: what the 'coeffs' and 'bounds' parameters mean, how solutions are returned (e.g., integer pairs, existence checks), computational complexity, or limitations (e.g., handling large coefficients). For a mathematical solver with two parameters, 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 concise and front-loaded: the first sentence directly states the tool's purpose, and the parenthetical adds domain context without unnecessary elaboration. There's no wasted verbiage, making it efficient for quick understanding. However, the lack of detail on parameters and usage slightly limits its effectiveness.

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 quadratic Diophantine equations, the description is incomplete. With no annotations, no output schema, and 0% schema description coverage, it doesn't provide enough context for effective use. It misses crucial details like parameter meanings, solution format, error handling, and mathematical assumptions (e.g., integer constraints). For a specialized mathematical tool, this leaves too many unknowns.

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, so the schema provides no parameter documentation. The description doesn't explain what 'coeffs' and 'bounds' represent (e.g., that 'coeffs' is likely [a, b, c, d, e, f] and 'bounds' might define search ranges). Without this semantic clarification, the parameters remain cryptic, and the description fails to compensate for the schema's lack of 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 general quadratic Diophantine equation ax² + bxy + cy² + dx + ey + f = 0.' It specifies the verb ('solve') and the mathematical resource (quadratic Diophantine equation), making the intent unambiguous. However, it doesn't differentiate from sibling tools like 'solve_linear_diophantine' or 'count_solutions_diophantine', which is why it doesn't achieve 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 minimal usage guidance. The parenthetical '(Domain: arithmetic, Category: diophantine_equations)' offers some context about the tool's mathematical domain, but it doesn't explain when to use this tool versus alternatives (e.g., 'solve_linear_diophantine' for linear equations or 'count_solutions_diophantine' for counting solutions). There's no explicit guidance on prerequisites, constraints, 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.