gaussian_elimination

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 mentions the method and partial pivoting, which implies numerical stability behavior, but does not state whether it returns a solution vector, handles singular matrices, or has any failure modes. Some behavioral context is given but incomplete.

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?

One sentence, front-loaded with the action and method, zero waste. Every word earns its place.

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 single-parameter mathematical tool with no annotations and no output schema, the description is minimal. It does not cover return format, error conditions, or edge cases like non-square or singular matrices. Adequate but with clear gaps.

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 100%, so the schema already documents the matrix parameter including its format as an augmented matrix. The description adds no parameter-level detail beyond what the schema provides. Baseline 3 is appropriate.

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?

Specific verb (Solve), specific resource (system of linear equations), and specific method (Gaussian elimination with partial pivoting). This distinguishes it from siblings like linear_solve, matrix_inverse, and matrix_operate.

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 linear systems, but gives no explicit when-to-use guidance, no exclusions, and does not name alternative tools like linear_solve that might overlap.

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