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

With no annotations provided, the description carries the full burden of behavioral disclosure. It adds the useful trait that computations are 'exact rational' rather than floating-point, but it does not disclose dimension requirements, invalid-input behavior, numerical limitations, or which operations require which inputs.

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 no filler. The core subject ('exact rational matrix & vector algebra') is front-loaded and every word in the operation list adds useful information.

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?

This is a multi-operation tool with several parameters and zero parameter documentation. While an output schema exists, the description still leaves critical input-side gaps: the mapping from operations to arguments, the expected string format for 'operation', and constraints like square matrices for inverse or eigenvalues. It is not complete enough for reliable 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?

Schema description coverage is 0%, and the description does not map any of the listed operations to matrix_A, matrix_B, vector_u, or vector_v. The agent cannot determine which parameters are needed for determinant versus dot product, what values 'operation' accepts, or how vectors differ from matrices in this context.

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 identifies the domain (exact rational matrix and vector algebra) and enumerates the supported operations: multiply, determinant, inverse, transpose, trace, eigenvalues, dot/cross. This distinguishes it from sibling tools like cognitive.compute_number_theory or cognitive.solve_equation_system, though it lacks an explicit verb form.

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?

There is no guidance on when to use this tool versus alternatives, nor any mention of prerequisites such as square matrices for determinant/inverse or dimension compatibility for multiplication. An agent is left to infer appropriate usage from the operation list alone.

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