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IBM

MCP Math Server

by IBM

frequency_from_period

Convert wave period to frequency for analyzing wave properties in trigonometry and wave analysis.

Instructions

Calculate frequency from period and related wave properties. (Domain: trigonometry, Category: wave_analysis)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
periodYes
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 tool calculates frequency but does not describe how it handles invalid inputs (e.g., negative periods), units (e.g., seconds for period, Hz for frequency), or error conditions. This lack of detail makes it difficult for an agent to predict behavior accurately.

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, stating the purpose in a single sentence. It efficiently includes domain and category information without unnecessary details. However, it could be slightly improved by integrating usage hints to enhance clarity 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 tool's complexity (mathematical calculation with one parameter), lack of annotations, no output schema, and low schema coverage, the description is incomplete. It does not explain the calculation method (e.g., frequency = 1/period), return values, or error handling, leaving significant gaps for an agent to invoke it correctly.

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 ('period') with 0% description coverage, so the description must compensate. It mentions 'period' but does not explain its meaning, units, or constraints (e.g., must be positive). The description adds minimal semantics beyond the schema, so it meets the baseline for low coverage but doesn't fully clarify parameter usage.

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: 'Calculate frequency from period and related wave properties.' It specifies the verb ('calculate'), resource ('frequency'), and input ('period'), and mentions the domain ('trigonometry, wave_analysis'). However, it does not explicitly differentiate from sibling tools like 'angular_velocity_from_period_or_frequency' or 'wave_amplitude_analysis', which could cause confusion in selection.

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 but does not specify scenarios, prerequisites, or exclusions. For example, it does not clarify if it's for simple frequency calculation or when other wave properties are needed, leaving usage ambiguous.

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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