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IBM

MCP Math Server

by IBM

maclaurin_series

Compute Maclaurin series expansions for mathematical functions by providing derivatives, x-values, and term counts to approximate functions near zero.

Instructions

Compute Maclaurin series expansion (Taylor series around x=0) (Domain: numerical, Category: series)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
derivativesYes
xYes
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 states the tool computes a Maclaurin series expansion but doesn't describe any behavioral traits such as computational limits, error handling, output format, or performance characteristics. The description is minimal and lacks details on what the tool actually returns or how it behaves, which is insufficient for a tool with three parameters.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness3/5

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

The description is concise with a single sentence, but it's not optimally structured. It front-loads the core purpose but includes parenthetical clarifications and tags that could be integrated more smoothly. While not verbose, the lack of parameter or usage details makes it feel under-specified rather than efficiently informative.

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 series computation with three parameters), no annotations, no output schema, and 0% schema description coverage, the description is incomplete. It doesn't explain the parameters, return values, or behavioral context needed for effective use. The description alone is inadequate for a tool of this nature, failing to provide necessary operational details.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters1/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

The input schema has three parameters (derivatives, x, n) with 0% schema description coverage, meaning none are documented in the schema. The description adds no information about these parameters—it doesn't explain what 'derivatives' represents (e.g., list of derivative values?), what 'x' is used for, or what 'n' signifies (e.g., number of terms?). This leaves all parameters semantically undefined, failing to compensate for the lack of schema documentation.

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: 'Compute Maclaurin series expansion (Taylor series around x=0)', which specifies the verb ('compute') and resource ('Maclaurin series expansion'). It distinguishes from siblings by mentioning the specific type of series (Maclaurin vs. other series tools like binomial_series, power_series, or taylor_series), though it doesn't explicitly contrast them. The domain and category tags add context but don't fully differentiate from all siblings.

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 ('numerical') and category ('series'), but doesn't specify scenarios, prerequisites, or exclusions. For example, it doesn't clarify when to choose this over 'taylor_series' or other series-related tools in the sibling list, leaving usage entirely implicit.

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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