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IBM

MCP Math Server

by IBM

harmonic_partial_sum

Calculate partial sums of the harmonic series between specified start and end terms to analyze convergence and divergence in mathematical sequences.

Instructions

Calculate partial sum of harmonic series with given terms. (Domain: arithmetic, Category: harmonic_series)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
startYes
endYes
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 states the tool calculates a partial sum, implying a read-only operation, but does not cover important aspects like computational complexity, error handling, or output format. For a tool with no annotations, this is a significant gap in transparency.

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, consisting of a single sentence that directly states the tool's purpose. It avoids unnecessary details, though it could be more informative. The structure is efficient, with no wasted words.

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 complexity (mathematical calculation with two parameters), lack of annotations, 0% schema coverage, and no output schema, the description is incomplete. It does not address parameter meanings, behavioral traits, or result format, making it inadequate for effective tool 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 parameters 'start' and 'end' undocumented. The description mentions 'given terms' but does not explain what these parameters represent (e.g., integer indices, inclusive/exclusive ranges) or provide examples. This fails to compensate for the lack of schema documentation, leaving parameters 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 partial sum of harmonic series with given terms.' It specifies the verb ('calculate'), resource ('partial sum of harmonic series'), and scope ('with given terms'). However, it does not explicitly differentiate from sibling tools like 'harmonic_series' or 'harmonic_number', which might have overlapping functionality.

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 ('harmonic_series'), but does not specify use cases, prerequisites, or comparisons to sibling tools such as 'harmonic_series' or 'harmonic_number'. This leaves the agent without clear direction on tool 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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