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PolarisHub

Math-MCP

by PolarisHub

greatest_common_divisor

Calculate the greatest common divisor (GCD) of two integers within the safe integer range.

Instructions

Finds the greatest common divisor (GCD) of two safe integers

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
firstYes
secondYes
Behavior3/5

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 'safe integers' to clarify input constraints but does not disclose behavior for negative numbers, zero, or edge cases like GCD(0,0). The output format is also not described.

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 a single sentence with no wasted words, efficiently conveying the tool's purpose and input constraints.

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

Completeness3/5

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

The description does not mention the return value or handle edge cases. Although the tool is simple, the lack of output schema and missing behavioral details (e.g., handling negative numbers) leave gaps for an agent.

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?

With 0% schema description coverage, the description adds only the qualifier 'safe integers' beyond the schema's parameter names and ranges. Since the parameter names ('first', 'second') are self-explanatory, the added value is minimal but present.

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

Purpose5/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description clearly states the tool finds the greatest common divisor (GCD) of two safe integers, using a specific verb and resource. It distinguishes from sibling tools like 'least_common_multiple' and other arithmetic functions.

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

Usage Guidelines4/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

The description implies usage for calculating GCD between two integers, and the term 'safe integers' provides context about valid input range. However, it does not explicitly mention when to use this tool over alternatives like LCM or prime factorization.

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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