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IBM

MCP Math Server

by IBM

gcd

Calculate the Greatest Common Divisor of two integers using the Euclidean algorithm to find the largest number that divides both without remainder.

Instructions

Calculate the Greatest Common Divisor (GCD) of two integers using Euclidean algorithm. (Domain: arithmetic, Category: number_theory)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
aYes
bYes
Behavior2/5

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 mentions the algorithm ('Euclidean algorithm'), which adds some behavioral context, but does not disclose other traits such as error handling, input constraints (e.g., negative numbers), performance characteristics, or output format. For a tool with no annotations, this is a significant gap in transparency.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness5/5

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is highly concise and front-loaded, consisting of a single sentence that directly states the tool's purpose and method, followed by domain and category tags. There is no wasted verbiage, and every element serves a clear purpose, making it efficient and well-structured.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness2/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Given the complexity of a mathematical function with no annotations, no output schema, and low schema coverage, the description is incomplete. It lacks details on behavior, parameter semantics, return values, and error conditions. While concise, it does not provide enough context for an agent to fully understand and invoke the tool correctly.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters3/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

The input schema has 0% description coverage, with parameters 'a' and 'b' documented only as integers. The description does not add any semantic details about these parameters, such as their meaning, valid ranges, or examples. Since the schema coverage is low, the description fails to compensate, resulting in minimal added value beyond the basic schema.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose4/5

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 Greatest Common Divisor (GCD) of two integers using Euclidean algorithm.' It specifies the verb ('Calculate'), resource ('GCD'), and method ('Euclidean algorithm'), making it unambiguous. However, it does not explicitly differentiate from sibling tools like 'extended_gcd' or 'gcd' variants, which slightly limits its distinction.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines2/5

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 the domain ('arithmetic') and category ('number_theory'), but does not specify scenarios, prerequisites, or comparisons to sibling tools like 'extended_gcd' or 'is_coprime'. This leaves the agent without explicit usage context.

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

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