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IBM

MCP Math Server

by IBM

digital_product_sequence

Calculate the iterative digital product sequence for any integer, reducing it to a single digit or zero by repeatedly multiplying its digits.

Instructions

Generate sequence by repeatedly applying digital product until single digit or zero. (Domain: arithmetic, Category: iterative_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 iterative process and termination condition, but does not cover critical aspects like error handling (e.g., for negative inputs), performance characteristics (e.g., iteration limits), or output format. For a tool with no annotations, 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.

Conciseness4/5

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

The description is concise and front-loaded, stating the core functionality in one sentence. The domain and category in parentheses are additional but not wasteful. It avoids redundancy and is efficiently structured, though it could be slightly more informative without losing brevity.

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 0% schema description coverage for the single parameter, the description is incomplete. It explains the high-level process but omits details on input validation, output format, error conditions, and performance limits. For a tool with iterative behavior, this lack of context makes it insufficient for reliable use.

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 'n' with 0% description coverage, and the tool description adds no information about 'n' (e.g., its meaning, valid range, or constraints). With low schema coverage, the description fails to compensate, leaving the parameter undocumented. This is inadequate for a tool with a required parameter.

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 sequence by repeatedly applying digital product until single digit or zero.' It specifies the verb ('generate sequence'), resource ('digital product'), and termination condition ('until single digit or zero'). However, it does not explicitly differentiate from sibling tools like 'digital_persistence' or 'digital_root', which may involve similar concepts, so it misses full sibling distinction.

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 on prerequisites, typical use cases, or comparisons to sibling tools such as 'digital_persistence' or 'digital_root'. The domain and category hints ('arithmetic, iterative_sequences') are too vague to serve as practical usage guidelines.

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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