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IBM

MCP Math Server

by IBM

pell_sequence

Generate the first n Pell numbers for mathematical calculations and sequence analysis in recursive sequences.

Instructions

Generate the first n Pell numbers. (Domain: arithmetic, Category: recursive_sequences)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
nYes
Behavior2/5

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

With no annotations provided, the description carries full burden for behavioral disclosure. It only states what the tool does without mentioning any constraints (e.g., valid ranges for n, performance characteristics, error handling). For a computational tool with no annotation coverage, 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.

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. Every word earns its place, with no redundant information. The domain/category tags are efficiently appended without disrupting readability.

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, no annotations, and no output schema, the description is insufficient. It doesn't explain what Pell numbers are, the format of the output (e.g., list of integers), or any edge cases. For a tool with one parameter but zero schema description coverage, more context is needed for effective use.

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 description mentions 'first n Pell numbers', which implies the parameter 'n' controls the count of numbers generated. Since schema description coverage is 0%, the description adds basic meaning beyond the bare schema. However, it doesn't specify constraints like n being positive or integer-only (though the schema indicates integer type), keeping it at the baseline.

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 Pell numbers.' It specifies the verb ('Generate'), resource ('Pell numbers'), and scope ('first n'). However, it doesn't explicitly differentiate from sibling tools like 'pell_number' or 'pell_lucas_number', which prevents 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. While the domain/category tags ('arithmetic, recursive_sequences') give some context, there's no explicit mention of when to choose this over similar sequence generators like 'fibonacci_sequence' or 'lucas_sequence' among the siblings.

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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