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

With no annotations, the description carries the full burden of behavioral disclosure. It adds the useful fact that results are exact rational rather than approximate, but it does not disclose input constraints, error behavior, or representation of non-rational results such as eigenvalues.

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 compact sentence with the key behavioral qualifier ('exact rational') front-loaded and the supported operations listed after a colon. No filler or redundancy.

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 five-parameter tool with no annotations and no enum constraints, the description is too thin: an agent cannot determine which parameters each operation requires (e.g., determinant needs a single matrix, multiply needs two) or what constraints apply. The presence of an output schema covers return values but not the missing invocation logic.

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 0%, so the description must compensate for the five parameters. It hints that matrices and vectors are the operands and that dot/cross need two vectors, but it never ties operations to matrix_A, matrix_B, vector_u, or vector_v, nor explains required shapes or formats.

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 names a precise domain (exact rational matrix & vector algebra) and enumerates concrete operations (multiply, determinant, inverse, transpose, trace, eigenvalues, dot/cross), so an agent can tell what this tool computes. It does not explicitly differentiate itself from the similarly named sibling cognitive.matrix_algebra, so it misses the full sibling distinction.

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 domain is stated clearly, so an agent can infer that this tool is for matrix and vector algebra requests. However, there is no explicit guidance about alternatives, prerequisites, or when not to use this tool, leaving the routing decision mostly to inference.

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