List available functions

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

Beyond the readOnlyHint annotation, the description reveals important behavioral nuances: every function exists on all 8 engines but is computed via native primitives, so results may diverge at poles, branch cuts, or ties, and that divergence is intended backend behavior. This is rich, honest context that an agent needs before trusting listed functions.

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 front-loaded with purpose and return fields, then usage guidance, then filter options, then behavioral caveats. Every sentence earns its place; there is no filler or repetition of schema/annotation content.

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 simple read-only list tool with one optional parameter and no output schema, the description provides everything an agent needs: what it lists, what each entry contains, how to filter, how it relates to evaluate, and a warning about cross-engine divergence. No material gap remains.

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 schema already covers the single optional 'category' parameter at 100% coverage, so the baseline is 3. The description adds value by enumerating all valid category values (algebraic, trigonometric, hyperbolic, exponential, special, rounding, introspection), which is especially useful since the schema provides no enum constraint.

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 a specific verb and resource: 'List all mathematical functions available via the Ultimath API,' and explicitly lists the returned fields (name, arity, category, description). It clearly distinguishes itself from the sibling 'evaluate' tool by framing itself as the discovery step for functions to pass to evaluate.

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?

It explicitly tells the agent when to use this tool: 'Use this to discover what functions you can pass to the evaluate tool.' It names the sibling evaluate as the downstream consumer, but it does not explicitly state a when-not condition or directly contrast with evaluate in an 'instead' formulation.

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