multinomial

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

No annotations are provided, so the description carries full burden for behavioral disclosure. It states what the tool calculates but doesn't describe important behaviors: input constraints (e.g., non-negative integers?), output format, error handling, or computational limits. The description is purely declarative without operational 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 efficiently structured in a single sentence with a clarifying parenthetical. It wastes no words and gets directly to the point. However, the parenthetical 'Domain: arithmetic, Category: general' adds minimal value and could be more 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?

Given no annotations, 0% schema coverage, and no output schema, the description is inadequate for a mathematical computation tool. It doesn't explain the mathematical formula, input requirements, output format, or edge cases. For a tool with one parameter but zero schema documentation, this leaves too much undefined for reliable use.

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%, and the description provides no parameter information beyond the generic term 'numbers.' It doesn't explain what the array represents (e.g., group sizes for multinomial coefficient calculation), expected length, value constraints, or examples. The description fails to compensate for the complete lack of schema documentation.

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 the multinomial coefficient.' It specifies this is a generalization of the binomial coefficient for multiple groups, which helps distinguish it from simpler binomial tools. However, it doesn't explicitly differentiate from sibling tools like 'binomial_pmf' or 'binomial_cdf' beyond mentioning the generalization concept.

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 minimal usage guidance: it mentions the domain (arithmetic) and category (general), but offers no explicit when-to-use instructions, prerequisites, or alternatives. There's no indication of when to choose this over binomial tools or other combinatorial functions in the extensive sibling list.

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