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IBM

MCP Math Server

by IBM

is_triangular_number

Check if a number is a triangular number to verify if it can be expressed as the sum of consecutive integers starting from 1.

Instructions

Check if a number is a triangular number. (Domain: arithmetic, Category: basic_sequences)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
nYes
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 only states what the tool does ('Check if a number is a triangular number') without describing how it behaves: e.g., what input range is valid, whether it handles negative numbers, what the output looks like (likely boolean), or any error conditions. For a tool with zero annotation coverage, this is a significant gap in 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: a single sentence that directly states the tool's purpose, followed by domain/category metadata. There is zero wasted verbiage, and every word earns its place. The structure is clear and efficient, making it easy for an agent to parse quickly.

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 simplicity (one parameter, no annotations, no output schema), the description is incomplete. It doesn't explain the return value (likely boolean), input constraints, or error handling. While the tool is straightforward, the description lacks necessary context for reliable invocation, especially with no annotations to fill behavioral gaps.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters3/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

The input schema has one parameter 'n' of type integer with 0% description coverage. The tool description adds no parameter-specific information beyond implying 'n' is the number to check. Since schema coverage is low, the description doesn't compensate by explaining constraints (e.g., non-negative integers) or examples. However, with only one parameter, the baseline is higher, but the lack of additional semantics keeps it at a minimal viable score.

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: 'Check if a number is a triangular number.' It specifies the verb ('Check') and resource ('triangular number'), and the domain/category context helps distinguish it from siblings like 'triangular_number' (which likely generates triangular numbers) or 'is_perfect_square' (a different property test). However, it doesn't explicitly differentiate from 'triangular_numbers' or 'triangular_sequence' in the sibling list, which could be 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 mentions the domain ('arithmetic') and category ('basic_sequences'), but this is generic context rather than specific usage instructions. There's no mention of prerequisites, when-not-to-use scenarios, or comparisons to sibling tools like 'triangular_number' or 'triangular_numbers'.

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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