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IBM

MCP Math Server

by IBM

euclidean_norm

Calculate the Euclidean norm (L2 norm) of a vector to determine its magnitude in linear algebra applications.

Instructions

Calculate the Euclidean norm (L2 norm) of a vector (Domain: linear_algebra.vectors, Category: general)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
vectorYes
Behavior1/5

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. The description only states what the tool calculates, with no information about error handling, input validation, performance characteristics, or output format. For a mathematical computation tool with zero annotation coverage, this is a significant gap in behavioral transparency.

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. There is no wasted verbiage, and it efficiently communicates the core functionality. The structure is clear and to the point.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness1/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Given the complexity of a mathematical tool with no annotations, 0% schema description coverage, and no output schema, the description is incomplete. It fails to address key aspects like parameter details, behavioral traits, or return values. For a tool performing a vector norm calculation, this leaves too many unknowns for effective use.

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 one parameter ('vector') with 0% schema description coverage. The description does not add any meaning beyond the schema—it does not explain what the vector represents, its expected format (e.g., numeric values), dimensionality, or constraints. With low schema coverage and no compensatory details in the description, this is inadequate.

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 the Euclidean norm (L2 norm) of a vector.' It specifies the mathematical operation (calculate), the resource (Euclidean norm/L2 norm), and the input (a vector). However, it does not distinguish this from sibling tools like 'chebyshev_norm' or 'manhattan_norm', which are also vector norm calculations, so it lacks sibling differentiation.

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 (linear_algebra.vectors) and category (general), but this is generic context rather than explicit usage instructions. There is no mention of when to choose Euclidean norm over other norms or related vector operations, nor any prerequisites or exclusions.

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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