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IBM

MCP Math Server

by IBM

bell_sequence

Generate Bell numbers for combinatorial mathematics calculations. This tool computes the first n Bell numbers, which count partitions of a set, supporting arithmetic and combinatorial analysis.

Instructions

Generate the first n Bell numbers. (Domain: arithmetic, Category: combinatorial_numbers)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
nYes
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 the tool generates Bell numbers but does not disclose behavioral traits such as computational complexity, input constraints (e.g., valid range for 'n'), error handling, or output format. This leaves significant gaps for a tool with a single parameter.

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 that directly states the tool's purpose. It is front-loaded with the core functionality and includes domain/category context efficiently, with no wasted words.

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 no annotations, no output schema, and low schema coverage, the description is incomplete. It lacks details on behavior, parameter constraints, and return values, which are critical for a computational tool. The domain/category hint is helpful but insufficient for full understanding.

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 0% description coverage, with parameter 'n' undocumented. The description mentions 'the first n Bell numbers', implying 'n' is a count, which adds basic semantics. However, it does not specify constraints (e.g., n must be positive integer) or examples, providing only minimal 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 the first n Bell numbers.' It specifies the verb ('Generate') and resource ('Bell numbers'), and includes domain/category context. However, it does not explicitly differentiate from sibling tools like 'bell_number' or 'bell_triangle', which appear related.

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 lacks any mention of prerequisites, typical use cases, or comparisons to sibling tools (e.g., 'bell_number' or 'bell_triangle'), leaving the agent without context for tool selection.

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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