solve_linear_system_2x2

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

There are no annotations provided. The description discloses that the tool handles no-solution and infinite-solution cases, which is useful behavioral context. However, it does not describe what the return value looks like (e.g., a struct, an array, error codes), leaving a gap in transparency.

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 sentence that conveys the core functionality and edge cases without unnecessary words. It is front-loaded with the primary purpose and efficiently communicates the tool's scope.

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 simple mathematical tool, the description covers the essential functionality and special cases. However, since there is no output schema, the lack of information about the return format or structure is a notable gap. The description could be more complete by hinting at what the result looks like.

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%, and the description provides no individual parameter details. However, the parameter names (a1, b1, c1, etc.) combined with the explicit equation in the description make their roles clear. This compensates moderately, but explicit parameter documentation would strengthen 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 solves a 2x2 linear system of the form a1*x + b1*y = c1 and a2*x + b2*y = c2. It also mentions handling no-solution and infinite-solution cases, which distinguishes it from other math tools like solve_quadratic or linear_regression.

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 implies usage for solving two linear equations but provides no explicit guidance on when to use this tool versus alternatives, nor does it mention when not to use it. Given the large set of sibling tools, more explicit usage context would be helpful.

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