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IBM

MCP Math Server

by IBM

digital_persistence

Calculate how many multiplication steps it takes to reduce a number to a single digit by repeatedly multiplying its digits.

Instructions

Calculate digital persistence (number of steps to reach single digit). (Domain: arithmetic, Category: special_numbers)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
nYes
operationNomultiply
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 for behavioral disclosure. The description only states what the tool calculates, without mentioning any behavioral traits: no information about computational complexity, error handling, input constraints (e.g., negative numbers?), output format, or whether it's deterministic. For a tool with no annotations, this leaves significant gaps in understanding how it behaves.

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: a single sentence that directly states the tool's purpose, followed by a domain/category tag. There's zero wasted text, and every element (calculation definition, domain context) earns its place efficiently.

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 complexity (mathematical operation with two parameters), lack of annotations, 0% schema description coverage, and no output schema, the description is incomplete. It defines the concept but fails to provide necessary context about parameters, behavior, output, or relationship to sibling tools. For a tool with this level of structural underspecification, the description should do more to compensate.

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?

Schema description coverage is 0%, so the description must compensate for undocumented parameters. The description mentions 'digital persistence' but doesn't explain what parameters 'n' (integer) and 'operation' (string with default 'multiply') mean in this context. It doesn't clarify what 'n' represents (starting number?), what 'operation' does (multiplication of digits?), or what alternatives to 'multiply' might be. The description adds minimal semantic value beyond the bare 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: 'Calculate digital persistence (number of steps to reach single digit).' It specifies the verb ('calculate'), resource ('digital persistence'), and provides a concise definition. However, it doesn't explicitly differentiate from sibling tools like 'digital_root' or 'persistent_digital_root', which appear to be related concepts in the sibling list.

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 includes a domain/category tag ('Domain: arithmetic, Category: special_numbers'), but this is generic classification rather than practical usage advice. There's no mention of when to choose this over similar tools like 'digital_root' or 'persistent_digital_root' from the sibling list.

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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