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IBM

MCP Math Server

by IBM

continued_fraction_golden_ratio

Generate continued fraction representation of the golden ratio to a specified depth for mathematical analysis and visualization.

Instructions

Generate continued fraction representation of golden ratio: [1; 1, 1, 1, 1, 1, ...] (Domain: arithmetic, Category: mathematical_constants)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
depthYes
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 generates but doesn't disclose behavioral traits like computational complexity, error handling, output format, or whether it's deterministic. The description is minimal and lacks important operational context.

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 with zero wasted words. It's a single sentence that efficiently communicates the core purpose and includes helpful domain/category metadata. Every element serves a clear purpose.

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?

For a tool with no annotations, 0% schema coverage, and no output schema, the description is inadequate. It doesn't explain the required parameter, output format, or behavioral characteristics. Given the mathematical context and parameter requirement, more completeness is needed.

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 description must compensate. It mentions no parameters at all, while the input schema requires a 'depth' parameter. The description fails to explain what 'depth' means or how it affects the output, leaving a critical gap in parameter documentation.

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: 'Generate continued fraction representation of golden ratio' with a specific pattern '[1; 1, 1, 1, 1, 1, ...]'. It includes domain/category context, but doesn't explicitly differentiate from sibling tools like 'golden_ratio_cf' or 'compute_golden_ratio_continued_fraction'.

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?

No guidance is provided about when to use this tool versus alternatives. The description mentions the domain and category but gives no explicit usage context, prerequisites, or comparisons to sibling tools that might handle similar mathematical constant representations.

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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