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IBM

MCP Math Server

by IBM

cf_to_rational

Convert continued fractions to rational numbers for mathematical calculations and analysis.

Instructions

Convert continued fraction to rational number. (Domain: arithmetic, Category: continued_fractions)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
cfYes
Behavior2/5

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

No annotations are provided, so the description carries full burden. It states what the tool does but doesn't disclose behavioral traits: it doesn't mention input constraints (e.g., valid continued fraction formats), error handling, performance characteristics, or what the output looks like (since there's no output schema). This leaves significant gaps for an agent to understand how to use it correctly.

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 extremely concise—a single sentence followed by domain/category tags—with zero wasted words. It's front-loaded with the core purpose, making it easy to parse. Every element (the conversion statement and tags) adds value without redundancy.

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 (a mathematical conversion with 1 parameter), lack of annotations, no output schema, and 0% schema description coverage, the description is incomplete. It states the purpose but doesn't provide enough context for an agent to reliably invoke the tool, such as explaining parameter semantics, output format, or error conditions. The domain/category tags help slightly but don't fill these gaps.

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

Parameters2/5

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

Schema description coverage is 0%, so the schema only documents the parameter 'cf' as an array of integers without any semantic explanation. The description adds no parameter information beyond the tool's purpose—it doesn't explain what 'cf' represents, how the array should be structured, or provide examples. This fails to compensate for the low schema coverage.

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 verb ('Convert') and resource ('continued fraction to rational number'), making the purpose unambiguous. It also includes domain/category tags which help contextualize. However, it doesn't differentiate from potential siblings like 'rational_to_cf' (which appears in the sibling list) or explain how this conversion differs from other mathematical operations.

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. While the domain/category tags hint at context, there's no explicit mention of when this conversion is appropriate, what prerequisites exist, or how it relates to sibling tools like 'rational_to_cf' (the inverse operation) or other continued fraction tools in the list.

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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