math

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

Annotations already declare readOnlyHint=true and idempotentHint=true, covering the safety profile. The description adds a hard timeout (10 s) with a fallback, the need to cite results via [L-...], and the fact that solve returns verified substitutions. These go beyond annotations and are useful behavioral context.

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?

The description is long but densely packed. It front-loads the purpose, then compactly lists operations with examples. The structure uses bullet points and minimal prose. It includes multilingual keywords, which may be extraneous but do not bloat the core content. No redundant sentences; each earns its place.

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 16 parameters, 15 operations, and no output schema, the description covers parameter usage per operation, timeout behavior, citation, and a verification note for solve. The only gap is that return formats for operations other than solve are not specified. Overall, it provides enough to call the tool correctly for most cases.

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?

With schema_description_coverage at 0%, the description fully compensates by detailing each operation's relevant parameters: solve (expression, expressions, variables, domain), diff (variable, order), integrate (lower/upper), limit (point, direction), series (point, order), summation/product (lower, upper), matrix (matrix_op, matrix, matrix2), and nsolve (x0). It also notes that 'variable' can be omitted when only one symbol exists, adding meaning well beyond the schema.

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 states it performs 'Symbolic math with SymPy' and enumerates specific operations (solve, diff, integrate, limit, series, matrices). This clearly distinguishes it from numeric siblings like calc, and the verb+resource is specific. It is immediately obvious what the tool does.

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 description implies usage for symbolic math problems and references 'Syntax as in calc', but it does not explicitly state when not to use it or which alternative to use for numeric calculations. No exclusions or alternative hunt is provided, leaving selection partially implicit.

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