Compute the extended GCD of two integers to get Bézout coefficients and an optional modular inverse for solving Diophantine equations and modular arithmetic problems.
Compute the extended GCD of two integers, returning Bezout coefficients and optionally the modular inverse.
| Name | Required | Description | Default |
|---|---|---|---|
| a | Yes | First integer | |
| b | Yes | Second integer |
Changes observed during successful MCP inspections.
v0.1.11Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full behavioral burden. It does disclose the return content (Bezout coefficients, modular inverse), which is the key trait for a pure math function, but it omits any note on failure cases (e.g., no inverse exists when gcd(a,b) != 1) or error behavior.
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?
A single front-loaded sentence that leads with the operation and ends with the return values. No padding or redundancy, though it could be split for clarity around the optional inverse.
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?
With no output schema, the description must cover return values, and it does so briefly. However, it promises an optional modular inverse while the input schema exposes only required a and b with no controlling option, leaving the agent unsure how that return is triggered.
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 100% with both parameters ('First integer', 'Second integer') documented in the schema, so the baseline of 3 applies. The description adds no constraints or semantics for a and b beyond what the schema already states.
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?
States a specific verb ('Compute') and resource ('extended GCD of two integers') and enumerates the returns ('Bezout coefficients and optionally the modular inverse'). It is distinguishable from siblings like gcd_calculate and gcd_lcm_calc, though it never explicitly contrasts itself with them.
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?
There is no guidance on when to prefer this over gcd_calculate, modular_arithmetic, or chinese_remainder, nor any stated preconditions for use. The reader must infer the use case entirely from the term 'extended GCD'.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.