math_quadratic_solver

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

No annotations are provided, so the description must disclose behavioral traits. It lists the various forms the solver provides (roots, discriminant, vertex, etc.), indicating the tool computes and returns these. However, it does not mention error handling, edge cases (e.g., a=0), or any side effects, leaving some 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 relatively short and front-loads the key purpose. However, it includes 'Menu ID: quadratic_solver' which is redundant with the tool name. Otherwise, it is efficiently written.

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 has 4 required parameters with no schema descriptions, no output schema, and no annotations, the description is incomplete. It fails to explain the 'operation' parameter and does not describe the return format or provide examples. The reference to describe_tool partially mitigates this, but the description itself is insufficient.

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?

Schema coverage is 0%, and the description does not explain the 'operation' parameter at all. While 'a', 'b', 'c' are implied to be coefficients, the lack of explanation for 'operation' (e.g., what values it accepts) significantly reduces clarity. The description adds minimal meaning beyond the schema.

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 as a 'Quadratic Equation Solver' and lists specific outputs (real/complex roots, discriminant, vertex form, etc.), making its purpose very clear and distinguishing it from sibling math tools.

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 suggests using describe_tool for full guidance but does not provide explicit when-to-use or when-not-to-use instructions. It lacks context on when this tool is appropriate compared to other solvers or mathematical tools.

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