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IBM

MCP Math Server

by IBM

ulam_spiral_analysis

Generate data for visualizing prime number patterns using the Ulam spiral to analyze mathematical sequences and identify prime distributions.

Instructions

Generate data for Ulam spiral prime visualization. (Domain: arithmetic, Category: prime_analysis)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
sizeYes
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 states the tool generates data for visualization, implying a read-only operation that outputs structured data, but doesn't disclose behavioral traits such as computational complexity, output format, error handling, or any side effects. This is inadequate for a tool with no annotation coverage.

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 with the core purpose in a single sentence, followed by domain/category tags. There's no wasted text, but it could be more structured (e.g., separating usage notes).

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 prime visualization, no annotations, 0% schema coverage, and no output schema, the description is incomplete. It doesn't explain what the output contains, how the Ulam spiral is constructed, or any limitations (e.g., performance with large sizes). This leaves significant gaps for an AI agent to use the tool effectively.

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?

The input schema has 1 parameter with 0% description coverage, and the tool description doesn't mention the parameter at all. It fails to explain what 'size' represents (e.g., spiral dimensions, number of primes, grid size) or provide any semantic context, leaving the parameter undocumented.

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 data for Ulam spiral prime visualization.' It specifies the action ('generate data') and the resource ('Ulam spiral prime visualization'), and includes domain/category context. However, it doesn't differentiate from sibling tools like 'prime_counting_function' or 'prime_density_analysis' that might also involve prime number analysis.

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 and category but doesn't indicate specific scenarios, prerequisites, or comparisons to sibling tools like 'sieve_of_eratosthenes' or 'prime_factors' that might be relevant for prime-related tasks.

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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