extended_gcd_bezout

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

With no annotations provided, the description carries full burden but offers minimal behavioral insight. It mentions 'multiple representations' which suggests the tool might return different formats, but doesn't clarify what these are, whether computations are exact or approximate, error handling, or performance characteristics. For a mathematical tool with potential complexity, this is inadequate.

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 extremely concise—a single sentence with no wasted words. It front-loads the core functionality ('Extended GCD with Bézout coefficients') and adds supplementary context ('multiple representations') efficiently. The domain/category annotation is separate and doesn't clutter the main description.

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 insufficient for a tool with 3 parameters and mathematical complexity. It doesn't explain return values, error conditions, or the 'multiple representations' feature. The agent lacks critical context to use this tool effectively beyond guessing from the name.

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 the description must compensate but adds no parameter information. It doesn't explain what 'a' and 'b' represent (e.g., integers for GCD computation), the purpose of 'find_alternatives', or any constraints (e.g., non-negative, non-zero). This leaves parameters undocumented beyond their basic types.

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 performs 'Extended GCD with Bézout coefficients and multiple representations,' specifying the mathematical operation (extended GCD), outputs (Bézout coefficients), and feature (multiple representations). It distinguishes from the simpler 'extended_gcd' sibling tool by mentioning additional representations, though it doesn't explicitly contrast with other GCD-related tools like 'gcd' or 'bezout_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?

No explicit guidance on when to use this tool versus alternatives is provided. The description mentions 'multiple representations' which hints at broader functionality than basic extended GCD, but doesn't specify use cases, prerequisites, or compare it to siblings like 'extended_gcd' or 'bezout_identity'.

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