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IBM

MCP Math Server

by IBM

element_wise_multiply

Multiply two vectors element-wise using the Hadamard product to compute pairwise multiplication of corresponding elements in linear algebra operations.

Instructions

Multiply two vectors element-wise (Hadamard product) (Domain: linear_algebra.vectors, Category: general)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
vector_aYes
vector_bYes
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. It mentions the operation type but does not disclose behavioral traits such as input validation (e.g., vector length matching), error handling, performance characteristics, or output format. The description is minimal and lacks necessary operational details.

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 with no wasted words, front-loading the core operation. It efficiently communicates the purpose in a single sentence, though this brevity contributes to gaps in other dimensions.

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 mathematical operation with 2 parameters, 0% schema coverage, no annotations, and no output schema, the description is inadequate. It lacks details on input validation, output format, error conditions, and usage context, making it incomplete for reliable tool invocation.

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%, and the description does not add any parameter semantics beyond naming 'vector_a' and 'vector_b'. It does not explain what these vectors represent, their expected format (e.g., numeric strings), length requirements, or constraints, leaving parameters largely undocumented.

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 verb ('Multiply') and resource ('two vectors element-wise'), and specifies the mathematical operation as 'Hadamard product'. However, it does not explicitly differentiate from sibling tools like 'multiply' (which might be scalar multiplication) or 'dot_product', though the domain/category context helps.

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 like 'multiply', 'dot_product', or 'element_wise_divide'. The domain/category tags offer some context but no explicit usage instructions, 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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