mobius_function_range

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

No annotations are provided, so the description carries the full burden. It mentions efficiency but doesn't disclose behavioral traits like computational complexity, memory usage, error handling, or output format. For a mathematical function tool with no structured safety hints, this leaves the agent guessing about performance and reliability.

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 concise and front-loaded with the core purpose in the first sentence. The domain/category in parentheses is slightly redundant but not wasteful. It avoids fluff and stays focused, though it could be more informative without losing brevity.

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 no annotations, 0% schema description coverage, and no output schema, the description is incomplete. It doesn't explain what the tool returns (e.g., list of values, dictionary mapping), error conditions, or performance characteristics. For a computational tool with one parameter, this leaves significant gaps in understanding how to use it effectively.

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 input schema has 1 parameter 'n' with 0% description coverage (no schema descriptions). The tool description adds no parameter semantics—it doesn't explain what 'n' represents (e.g., upper bound of range, range size, or starting point), valid ranges, or units. This is inadequate given the low schema coverage.

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's purpose: 'Calculate Möbius function values for a range of numbers efficiently.' It specifies the verb ('calculate'), resource ('Möbius function values'), and scope ('range of numbers'), though it doesn't explicitly differentiate from its sibling 'mobius_function' (which likely calculates for a single number). The domain/category tags add context but aren't part of the core description.

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 provides no guidance on when to use this tool versus alternatives. It doesn't mention the sibling 'mobius_function' (for single values) or 'apply_mobius_inversion' (for applying the inversion formula), nor does it specify prerequisites like input constraints or typical use cases. The efficiency claim is vague and not actionable.

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