linear_algebra

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

Beyond the readOnly/idempotent/non-destructive annotations, the description adds rich behavioral context: exact arithmetic, the 25x25 matrix size limit, preservation of exact fractional string entries, and numerical-stability warnings for condition numbers. No contradiction with annotations.

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 short, information-dense sentences, front-loaded with the core purpose and followed by practical details. Every sentence earns its place and there is no filler or tautology.

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?

The description covers key constraints and behavioral caveats for a complex matrix tool, while the output schema handles return details. It omits precision semantics and explicit alternative-tool guidance, but the operation enum and annotations fill many gaps.

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 description clarifies matrix (size limit, exact string entries) and other_matrix (multiplication or solve RHS), but the precision parameter is not explained. Since schema description coverage is 0%, the description only partially compensates for the lack of parameter documentation.

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 performs exact matrix/linear-algebra operations on matrices up to 25x25, and mentions matrix inputs, other_matrix, and condition-number warnings. It does not explicitly contrast with sibling tools like solve or calculate, so it misses the full sibling-differentiation criterion.

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?

Usage context is implied: the tool is for exact matrix operations. It gives parameter-level guidance (other_matrix for multiplication or solve RHS, string entries preserve exact values), but it does not state when to choose this tool over alternatives or mention exclusions.

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