matrix_det_2x2

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 calculation action but does not describe any behavioral traits such as error handling (e.g., invalid matrix inputs), computational limits, or output format. For a tool with zero annotation coverage, this is a significant 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 extremely concise and front-loaded, stating the core purpose in a single sentence. The additional domain and category information is minimal and does not detract from clarity. There is no wasted verbiage, making it efficient for quick understanding.

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 a mathematical calculation tool with no annotations, 0% schema description coverage, and no output schema, the description is incomplete. It lacks essential details such as parameter explanations, error conditions, and return value information, which are necessary for effective tool use.

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 schema description coverage is 0%, meaning the input schema provides no descriptions for the 'matrix' parameter. The description does not compensate by explaining the parameter's semantics, such as the expected format (e.g., a 2x2 array of numbers as strings), constraints, or examples. This leaves the parameter poorly documented.

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: 'Calculate the determinant of a 2x2 matrix.' It specifies the verb ('calculate'), resource ('determinant'), and scope ('2x2 matrix'), making the function unambiguous. However, it does not explicitly differentiate from sibling tools like 'matrix_det_3x3' or 'matrix_solve_2x2', which would require a 5.

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 no guidance on when to use this tool versus alternatives. It mentions the domain ('linear_algebra.matrices') and category ('general'), but this is not actionable usage advice. There is no mention of prerequisites, limitations, or comparisons to sibling tools like 'matrix_det_3x3' or 'matrix_solve_2x2'.

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