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IBM

MCP Math Server

by IBM

normalize_vector

Convert any vector to unit length by scaling its components. This tool handles vectors of any dimension and provides adjustable precision for normalization calculations.

Instructions

Normalize a vector to unit length (Domain: linear_algebra.vectors, Category: general)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
vectorYes
norm_typeNo
toleranceNo
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 action ('normalize') but does not explain what normalization entails (e.g., scaling by magnitude), potential errors (e.g., handling zero vectors), or output format. For a tool with 3 parameters and no annotations, this leaves significant gaps in understanding its behavior and constraints.

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—a single sentence—and front-loaded with the core purpose. Every word earns its place, and there is no redundancy or unnecessary elaboration. It efficiently communicates the essential action without waste.

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 (3 parameters, no annotations, no output schema), the description is incomplete. It lacks details on parameters, behavioral traits (e.g., error handling), and output expectations. While conciseness is high, the description does not provide enough context for an agent to use the tool effectively without additional inference or trial.

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 schema description coverage is 0%, meaning parameters are undocumented in the schema. The description does not mention any parameters ('vector', 'norm_type', 'tolerance') or their roles, such as what 'norm_type' (default 2) or 'tolerance' (default 1e-10) mean. With 3 parameters and no compensation 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: 'Normalize a vector to unit length.' It specifies the verb ('normalize'), resource ('vector'), and outcome ('unit length'), which is precise. However, it does not distinguish this tool from its many siblings, such as 'vector_norm' or 'euclidean_norm', which might have overlapping or related functionality, 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 a domain ('linear_algebra.vectors') and category ('general'), but these are generic and do not specify use cases, prerequisites, or exclusions. Without explicit when/when-not instructions or named alternatives, the agent must infer usage from context alone.

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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