multiplicative_function_analysis

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

No annotations are provided, so the description carries full burden. It mentions 'analyze' but doesn't disclose what the tool actually does behaviorally - whether it computes values, applies inversion, returns analytical results, or something else. No information about output format, computational limits, or error conditions.

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 - one sentence plus domain/category tags. It's front-loaded with the core purpose. However, the conciseness comes at the cost of completeness, making it under-specified rather than efficiently informative.

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 tool with 2 parameters (0% schema coverage), no annotations, no output schema, and multiple overlapping sibling tools, the description is completely inadequate. It doesn't explain what analysis means, what parameters do, what results to expect, or when to choose this over similar tools.

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 description coverage is 0%, so parameters are completely undocumented in the schema. The description provides no information about what 'function_name' should be (named multiplicative functions like Euler's totient, divisor function, etc.) or what 'range_end' controls (evaluation range, inversion limit). No parameter guidance whatsoever.

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 the tool 'Analyze multiplicative functions using Möbius techniques' which provides a general purpose (analyze with specific techniques). However, it's vague about what 'analyze' entails - computational properties, range evaluation, or inversion applications. The domain/category tags add context but don't clarify the specific action.

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?

No guidance on when to use this tool versus alternatives. With sibling tools like 'mobius_function', 'mobius_function_range', 'mobius_inversion_formula', and 'apply_mobius_inversion', there's clear overlap but no differentiation. The description doesn't indicate whether this is for evaluation, inversion, or range analysis of multiplicative functions.

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