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IBM

MCP Math Server

by IBM

vector_projection

Calculate the projection of one vector onto another to find component magnitude and direction in linear algebra applications.

Instructions

Project one vector onto another (Domain: linear_algebra.vectors, Category: general)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
vector_aYes
vector_bYes
Behavior1/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

No annotations are provided, so the description must fully disclose behavioral traits. It fails to mention any behavioral aspects such as input validation (e.g., vector dimensions, numeric types), error handling, computational complexity, or output format. This leaves critical operational details unspecified.

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 with the core purpose in a single sentence, followed by domain and category. It avoids unnecessary details, though it could be more informative without sacrificing brevity.

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 of a vector projection operation, no annotations, no output schema, and 0% schema description coverage, the description is incomplete. It lacks essential details such as the mathematical formula, return type (e.g., vector or scalar), error conditions, and examples, making it inadequate for reliable use.

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 schema description coverage is 0%, so the description must compensate by explaining parameters. It does not describe 'vector_a' and 'vector_b' beyond their names, failing to clarify their roles (e.g., which is projected onto which), expected formats (e.g., numeric arrays), or constraints (e.g., same length). This adds minimal value over the schema.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose3/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description states the tool's purpose as 'Project one vector onto another' with a domain and category, which is clear but vague. It specifies the verb ('Project') and resource ('vector'), but does not distinguish it from sibling tools like 'scalar_projection' or 'vector_rejection' that might perform related operations, leaving the exact mathematical operation ambiguous.

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 lacks explicit instructions, prerequisites, or comparisons to sibling tools such as 'scalar_projection' or 'vector_rejection', leaving the agent without context for 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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