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IBM

MCP Math Server

by IBM

golden_ratio_cf

Calculate continued fraction expansions of the golden ratio φ for specified numbers of terms using mathematical computation.

Instructions

Generate continued fraction expansion of golden ratio φ. (Domain: arithmetic, Category: continued_fractions)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
termsYes
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 of behavioral disclosure. It states the tool generates a continued fraction expansion but does not explain what the output looks like (e.g., format, length, precision), whether it's deterministic, or if there are any limitations (e.g., maximum terms). For a computational tool with no annotations, this leaves significant gaps in understanding its behavior.

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

Conciseness4/5

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

The description is concise and front-loaded, stating the core functionality in the first sentence. The parenthetical metadata ('Domain: arithmetic, Category: continued_fractions') is slightly extraneous but not wasteful. Overall, it is efficiently structured with no redundant phrasing.

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 tool's computational nature, lack of annotations, no output schema, and minimal parameter documentation, the description is incomplete. It does not explain the output format, behavioral traits, or usage context, which are critical for an agent to invoke it correctly. The description alone is insufficient for effective tool use without external assumptions.

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 1 parameter ('terms') with 0% description coverage, so the schema provides no semantic context. The description does not mention parameters at all, failing to compensate for the schema's lack of documentation. However, since there is only one parameter and its purpose (number of terms) is somewhat inferable from the tool's name and description, it meets the baseline for minimal viability without adding value beyond the 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: 'Generate continued fraction expansion of golden ratio φ.' It specifies the verb ('Generate'), resource ('continued fraction expansion'), and target ('golden ratio φ'), making the function unambiguous. However, it does not explicitly differentiate from sibling tools like 'continued_fraction_golden_ratio' or 'compute_golden_ratio_continued_fraction', which appear to serve similar purposes, preventing a perfect score.

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 a 'Domain' and 'Category' in parentheses, but this is generic metadata rather than practical usage advice. There is no indication of prerequisites, constraints, or comparisons to sibling tools like 'continued_fraction_golden_ratio', leaving the agent without clear direction.

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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