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IBM

MCP Math Server

by IBM

matrix_add

Add two matrices element-wise to perform matrix addition operations in linear algebra.

Instructions

Add two matrices element-wise (Domain: linear_algebra.matrices, Category: general)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
matrix_aYes
matrix_bYes
Behavior2/5

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

No annotations are provided, so the description carries full burden. It mentions 'element-wise' which clarifies the addition behavior, but fails to disclose critical behavioral traits: it doesn't specify that matrices must have the same dimensions, doesn't mention error handling for mismatched sizes, doesn't describe the return format (e.g., a matrix array), and doesn't address numerical precision or overflow concerns.

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 appropriately concise with a single sentence that front-loads the core purpose ('Add two matrices element-wise'). The domain/category annotation is efficiently appended. There's no wasted verbiage, though it could benefit from slightly more detail given the lack of annotations and schema descriptions.

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 matrix operations, no annotations, 0% schema description coverage, and no output schema, the description is incomplete. It lacks essential context: matrix format expectations, dimension matching requirements, error conditions, return value structure, and numerical considerations. The domain/category hint helps but doesn't compensate for these gaps.

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?

Schema description coverage is 0%, so the description must compensate. It mentions 'two matrices' which aligns with the two parameters (matrix_a, matrix_b), but adds no semantic details beyond what the parameter names imply: no explanation of matrix format (2D arrays of strings representing numbers), no dimension requirements, no examples, and no constraints on element values.

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: 'Add two matrices element-wise' specifies the verb (add) and resource (matrices) with the operation type (element-wise). It distinguishes from siblings like 'matrix_multiply' and 'matrix_subtract' by specifying element-wise addition, but doesn't explicitly differentiate from 'add' (which appears to be scalar addition) or 'vector_add'.

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 minimal guidance with the domain/category annotation ('Domain: linear_algebra.matrices, Category: general'), but offers no explicit when-to-use instructions, no mention of prerequisites (e.g., matrix dimensions must match), and no alternatives for when this tool is inappropriate versus other matrix operations like 'matrix_multiply' or 'matrix_subtract'.

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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