bezout_identity

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 states what the tool computes (Bézout coefficients) but doesn't disclose behavioral traits like input constraints (e.g., handling of negative integers, zero values), computational characteristics (e.g., performance with large numbers), error conditions, or output format. For a mathematical tool with no annotation coverage, this leaves significant gaps in understanding how it behaves.

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 appropriately concise with two sentences. The first sentence clearly states the purpose, and the second provides domain/category context. There's no wasted text, and the key information is front-loaded. The parenthetical domain/category could be considered slightly extraneous but doesn't significantly detract from efficiency.

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 of a mathematical computation tool with no annotations, 0% schema description coverage, and no output schema, the description is incomplete. It states what is computed but doesn't cover important aspects like input validation, error handling, output format (e.g., how coefficients are returned), or performance considerations. For a tool that solves a non-trivial mathematical problem, more context is needed for effective 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?

The description doesn't explicitly mention parameters, but it implicitly defines 'a' and 'b' through the equation 'ax + by = gcd(a, b)'. With 0% schema description coverage (no parameter descriptions in the schema), the description adds some semantic meaning by indicating these are integers in a Bézout identity context. However, it doesn't provide details like valid ranges, special cases (e.g., zero or negative values), or examples, so it only partially compensates for the schema gap.

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: 'Find Bézout coefficients: integers x, y such that ax + by = gcd(a, b).' It specifies the verb ('Find'), the resource ('Bézout coefficients'), and the mathematical relationship. It distinguishes from siblings like 'extended_gcd' and 'extended_gcd_bezout' by explicitly naming the Bézout identity.

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 mentions 'Domain: arithmetic, Category: bezout_identity' which gives some context but doesn't specify when to choose this over similar tools like 'extended_gcd' or 'extended_gcd_bezout' that likely compute related values. No explicit when/when-not statements or alternatives are provided.

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