math_matrix_calculator

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

Discloses beyond annotations: runs locally, read-only and non-destructive (consistent with annotations), rate-limited (60 requests/min for anonymous), algorithm details for determinant (cofactor vs LU). While annotations already provide readOnlyHint/destructiveHint, description adds operational context like rate limit and local execution. No contradictions.

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?

Well-structured: begins with a summary of operations, then preconditions, then sibling alternatives, and finally behavioral notes. Sentences are efficient but some redundancy exists (e.g., repeated mention of 'finite-precision'). Front-loaded with the tool's core purpose. Could be slightly shorter, but effective overall.

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?

Given the tool's complexity (8 operations, multiple preconditions, siblings), the description covers all necessary aspects: operations list, preconditions, alternatives, rate limit, return types. Output schema exists, so return format detail is sufficient. No gaps in guidance for the agent to misuse the tool.

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 100% with each parameter described, so baseline is 3. Description adds meaningful context by grouping parameters per operation and stating preconditions (e.g., 'add/subtract need equal dimensions', 'inverse needs non-singular matrix'), which is not enforced in the schema alone. This additional guidance helps parameter selection.

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?

Describes specific verb+resource: 'Matrix Calculator' performing finite-precision linear-algebra operations on small matrices. Lists all operations explicitly (add, subtract, multiply, scalarMultiply, transpose, determinant, inverse, identity) and distinguishes from siblings by naming alternatives (math_scientific_calculator, math_statistics_calculator, math_quadratic_solver).

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?

Provides clear when-to-use context by listing preconditions (e.g., equal dimensions for add/subtract, square matrix for determinant/inverse). Explicitly states when not to use by suggesting alternatives for scalar expressions, statistics, and polynomial roots. Covers both inclusion and exclusion criteria.

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