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IBM

MCP Math Server

by IBM

narayana_cow_number

Calculate Narayana's cow sequence values for modeling reproductive populations in mathematical biology and recursive sequence analysis.

Instructions

Calculate Narayana's cow sequence (cows that reproduce). (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 the full burden of behavioral disclosure. It mentions the sequence involves 'cows that reproduce,' hinting at a recursive or generative process, but fails to detail computational behavior (e.g., recursion depth, performance, or output format). This is inadequate for a tool with no structured annotations.

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 and front-loaded, consisting of a single sentence that directly states the tool's purpose and domain. There is no wasted verbiage, making it efficient for quick comprehension.

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?

For a tool with no annotations, 0% schema coverage, and no output schema, the description is insufficient. It lacks details on parameter meaning, behavioral traits, return values, and usage context, making it incomplete for effective agent invocation.

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 0% description coverage, with one required parameter 'n' of type integer. The description does not explain what 'n' represents (e.g., term index, count of cows) or its constraints (e.g., range, typical values). Given the low schema coverage, the description fails to compensate, leaving the parameter's meaning ambiguous.

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: 'Calculate Narayana's cow sequence (cows that reproduce).' It specifies the verb ('calculate'), resource ('Narayana's cow sequence'), and provides domain/category context. However, it does not explicitly differentiate from sibling tools like 'narayana_number' or 'narayana_triangle_row', which are related but distinct, so it falls short of 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 lacks context about typical use cases, prerequisites, or comparisons to sibling tools (e.g., 'narayana_number' or 'narayana_triangle_row'), leaving the agent without direction for 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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