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IBM

MCP Math Server

by IBM

lucas_sequence

Generate the first n Lucas numbers to analyze recursive sequences in arithmetic contexts. This mathematical tool calculates the Lucas sequence for specified values.

Instructions

Generate the first n Lucas 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?

No annotations are provided, so the description carries full burden. It states the tool generates numbers but doesn't disclose behavioral traits: it doesn't mention what 'n' represents (e.g., non-negative integer, maximum value), whether it returns a list or single value, error handling for invalid inputs, or performance characteristics. The description is minimal and lacks critical 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.

Conciseness4/5

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

The description is concise and front-loaded: the first sentence states the core purpose clearly. The second sentence adds domain/category context efficiently. There's no wasted text, and it's appropriately sized for a simple tool. However, it could be slightly more structured by 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 no annotations, 0% schema coverage, and no output schema, the description is incomplete. It doesn't explain what the tool returns (e.g., a list of integers), handle edge cases, or provide examples. For a tool with one parameter but undefined behavior and output, more detail is needed to ensure correct agent invocation.

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?

Schema description coverage is 0%, so the description must compensate. It mentions 'the first n Lucas numbers', implying 'n' is the count of numbers to generate, which adds meaning beyond the schema's bare 'integer' type. However, it doesn't specify constraints (e.g., n >= 0), format, or examples, leaving gaps. With one parameter and low coverage, this provides basic but incomplete semantics.

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 Lucas numbers' with a specific verb ('Generate') and resource ('Lucas numbers'). It distinguishes from siblings like 'lucas_number' (singular) and 'lucas_u_v' by specifying it generates a sequence of the first n numbers. However, it doesn't explicitly contrast with 'fibonacci_sequence' which is a closely related recursive sequence.

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 ('arithmetic') and category ('recursive_sequences'), but gives no explicit when/when-not instructions, prerequisites, or comparisons to sibling tools like 'fibonacci_sequence' or 'lucas_number'. Usage is implied by the name and purpose alone.

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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