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

Annotations already declare readOnlyHint=true and idempotentHint=true, so the safety profile is covered. The description adds nothing beyond that: the 'square matrix' requirement is already stated in the schema's parameter description, and there is no note on how non-square or oversized input is handled.

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?

A single front-loaded sentence with zero filler, properly sized for a one-parameter tool. It is efficient, though it leaves no room for the alternative-routing context a fuller definition would include.

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 low-complexity, single-parameter tool with full schema coverage, an output schema, and safety annotations, the definition covers what an agent needs to invoke correctly. Only input-error behavior (non-square matrices, dimension limits) is unstated.

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?

There is only one parameter and schema description coverage is 100%, with the schema documenting the nested row structure, example, and maxItems. The description adds no syntax or format detail beyond what the schema already provides, so the baseline 3 applies.

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?

Names a specific operation (calculate the determinant) on a specific resource (square matrix), which cleanly separates it from siblings like matrix_inverse, matrix_transpose, and matrix_multiply. It does not explicitly name those siblings as alternatives, but the verb+resource pairing is unambiguous.

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 gives no guidance on when to choose this tool over matrix_eigenvalues or matrix_inverse, nor any prerequisite context. It only implies usage from the resource type, with no explicit when/when-not conditions.

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