matrix_solve_3x3

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

No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the method ('Cramer's rule') but does not describe key behavioral traits such as numerical stability limitations, error handling for singular matrices, input format expectations (e.g., string arrays for numbers), or output structure. This leaves significant gaps for a tool that performs mathematical computations.

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 highly concise and front-loaded, consisting of a single sentence that directly states the tool's purpose and method. Every word earns its place, with no redundant or verbose language, making it efficient for an agent to parse quickly.

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 complexity of solving linear equations, lack of annotations, 0% schema coverage, and no output schema, the description is incomplete. It does not cover critical aspects like input validation, error cases (e.g., non-invertible matrices), output format, or performance considerations, leaving the agent under-informed for reliable tool invocation.

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 input schema has 0% description coverage, so the description must compensate. It does not explain the parameters 'matrix_a' and 'vector_b' beyond implying they represent the matrix A and vector b in Ax=b. No details on array dimensions (e.g., 3x3 for matrix_a, length 3 for vector_b), data types (strings likely for numerical values), or formatting are provided, failing to adequately clarify parameter semantics.

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: 'Solve a 3x3 system of linear equations Ax = b using Cramer's rule'. It specifies the verb ('solve'), resource ('3x3 system of linear equations'), and method ('Cramer's rule'). However, it does not explicitly differentiate from sibling tools like 'matrix_solve_2x2' or 'gaussian_elimination', which are also linear algebra solvers, so it falls short of a perfect score.

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 provides minimal usage guidance. It mentions the domain ('linear_algebra.matrices') and category ('general'), but does not specify when to use this tool versus alternatives (e.g., for 3x3 systems only, or when Cramer's rule is appropriate). No explicit when/when-not instructions or sibling tool comparisons are included, leaving the agent with little contextual direction.

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