math_number_theory

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

No annotations are present, so the description should disclose behavioral traits. It only describes input formats and basic functionality, but lacks any mention of error handling, performance characteristics, or limitations. For a tool with many operations, more transparency is needed.

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 relatively long but well-structured: first a line summarizing purpose, then value format rules, then a clear bullet list of operations. It is front-loaded with the purpose. While it could be more concise, the density of information justifies its length.

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 the complexity (20 operations, 2 parameters, output schema available), the description covers the input semantics comprehensively. It does not explain return values, but output schema exists. Minor gap: the default value of 'operation' (factor) is not mentioned. Overall, it is nearly complete.

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 coverage is 0%, so the description must compensate, which it does thoroughly. It explains the 'value' parameter format for each operation (e.g., '1234567890' for factor, '1234,5678' for GCD) and lists all operation options with brief descriptions. This adds essential meaning 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 clearly states it performs number theory operations ('数论运算') and lists 20 specific operations (factor, gcd, etc.). It distinguishes itself from sibling tools like math_calculus or math_eval by focusing exclusively on number theory calculations.

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 siblings. There is no mention of alternatives or contexts where other math tools would be preferred. The description only lists operations without usage heuristics.

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