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

No annotations are provided, so the description carries the full burden. It discloses only that equations are solved, but omits behavioral traits such as handling of complex roots, degenerate cases, or whether the solution returns steps or just results. The description adds no behavioral context beyond the bare capability.

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 a single, dense sentence that front-loads the primary action and lists the three supported cases. There is no fluff or repetition; it is maximally concise and well-structured.

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?

Despite having an output schema, the description is insufficient for correct invocation. It does not explain how to set parameters for each equation type (e.g., which fields to populate for linear vs quadratic vs system), nor does it clarify the required equation_type values. An agent would struggle to call this tool correctly without further information.

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 description coverage is 0% – the description never mentions parameters. While the schema titles (Quad A, Linear A, etc.) hint at usage, the description does not explicitly map the equation forms to the parameter groups or specify valid values for equation_type. The description adds little beyond what the schema already implies.

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 states a clear purpose: solve linear, quadratic, or linear systems, with explicit equation forms. It uses a specific verb (solve) and a resource (equation system) and distinguishes itself from sibling tools like cognitive_solve_arithmetic by specifying the exact types of equations handled.

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 given on when to use this tool versus alternatives. There are many sibling solve tools (solve_arithmetic, solve_word_problem, solve_and_compare), but the description does not mention any exclusions or selection criteria, leaving the agent to infer the appropriate context.

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