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XBP-Europe
by XBP-Europe

group_operation

Constructs a group from a SageMath expression and queries its properties: order, abelianness, cyclicity, center, conjugacy classes, and exponent.

Instructions

Group theory: construct groups and query properties (order, is_abelian, center, etc.)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
groupYesSage group constructor, e.g. 'SymmetricGroup(5)', 'DihedralGroup(4)', 'CyclicPermutationGroup(6)', 'AlternatingGroup(5)'
operationYesOne of: order, is_abelian, is_cyclic, center_order, conjugacy_classes_count, exponent

Output Schema

TableJSON Schema
NameRequiredDescriptionDefault

No arguments

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 the core action, omitting any details on error handling, side effects, safety, or limitations. For example, it does not clarify that the tool is read-only or what happens with invalid group constructors.

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 a single, focused sentence that front-loads the domain and action. Every word adds value, and it is appropriately sized for a simple domain-specific tool.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness4/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

For a simple two-parameter tool with an output schema, the description gives the essential context: the domain and the type of operations. It is complete enough for an agent to select the tool, though it lacks behavioral caveats that would require extra context given the absence of annotations.

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 covers both parameters with descriptions and examples (group constructors and operation list). The tool description adds minimal value beyond 'construct groups and query properties', which loosely maps to the parameters but does not elaborate on parameter syntax or allowed values beyond what the schema already provides. Baseline 3 is appropriate given 100% schema coverage.

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

Purpose5/5

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

The description clearly identifies the tool's domain ('Group theory') and its action ('construct groups and query properties'), with specific examples like order, is_abelian, center. This distinguishes it from sibling operations like matrix_operation and number_theory_operation.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines3/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

The description implies usage for group theory queries but does not explicitly state when to prefer this tool over alternatives or mention any exclusions. It lacks a 'use this for X, use that for Y' pattern, so guidance is only implied by the domain label.

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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