geometry.matrix_determinant

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

Annotations already declare readOnly/idempotent/closed-world, so the bar is lower, yet the description still adds real behavioral context: exact Decimal expansion for n ≤ 3 versus numpy float64 at ~15 digits for n ≥ 4, a hard size cap of 200, and an explicit error case for non-square matrices. It does not describe the response shape, but an output schema exists to cover that.

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?

Four compact sentences with the representation constraint front-loaded, followed by precision behavior and the error condition. Slight redundancy in the double caveat about n ≥ 4 approximateness, but no filler.

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 one-parameter numeric tool with an output schema and read-only annotations, the description covers input format, size limits, numerical precision tradeoffs, and the failure mode. Nothing an agent needs to call it correctly is absent.

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 coverage is 0% — the single parameter M is only typed as an array of arrays of strings. The description compensates by specifying the format (n×n 2D list of Decimal strings) and the size bound, which is exactly the missing 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?

States a specific verb and resource: computes the determinant of a square matrix M. It is plainly distinguishable from siblings like matrix_inverse and matrix_solve, which do different linear-algebra operations.

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?

Gives concrete usage conditions: input must be an n×n Decimal-string list with n ≤ 200, non-square input is an error, and n ≥ 4 returns an approximation. It does not name alternatives (e.g., matrix_solve for systems), but the applicability conditions are unambiguous.

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