solve_polynomial

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

No annotations are provided, so the description must carry the behavioral transparency burden. It discloses the degree limit (1–4) and the default allow_complex behavior, but it does not mention return format, error handling for invalid degrees, or how complex roots are represented. This is moderately transparent but leaves 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: three short lines covering when, parameters, and an example. Every sentence serves a purpose and the key information is front-loaded. No wasted words.

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 tool's simplicity, the description covers scope, parameters, and an example. An output schema exists, so return value details are not required. It could mention edge cases like out-of-range degrees, but the 'degree 1–4' qualification already sets expectations. Overall, the description is mostly complete for this task.

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 schema has zero description coverage, but the description fully compensates by explaining both parameters: coefficients as an ordered list a0...an and allow_complex as a boolean with default true. The example clarifies coefficient ordering with a concrete polynomial (x^2-2=0).

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: finding roots of a polynomial a0+…+an x^n with degree 1–4. It specifies the resource (polynomial) and the action (find roots), and distinguishes itself from general root-finding with 'not general f(x)'.

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 explicitly states when to use it: for polynomial roots of degree 1–4. It also provides a when-not case ('not general f(x)'), implying alternative tools (like solve_root) for general functions. This gives clear usage context.

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