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sympy_product_set

Compute the Cartesian product of multiple sets by providing comma-separated set expressions. This tool calculates all possible ordered combinations across the specified sets.

Instructions

Product of sets (comma-separated).

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
setsYes

Output Schema

TableJSON Schema
NameRequiredDescriptionDefault
resultYes
Behavior1/5

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

No annotations are provided, so the description must fully disclose behavioral traits. It only mentions the input format ('comma-separated') without explaining what the tool does (e.g., returns a set, performs a mathematical operation), potential side effects, error conditions, or output behavior. This leaves the agent with insufficient information to understand the tool's behavior.

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 a single phrase, 'Product of sets (comma-separated).' It is front-loaded and wastes no words, though this brevity contributes to its lack of detail. Every part of the sentence is relevant to the tool's function.

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 mathematical operations and the lack of annotations, the description is incomplete. It does not clarify the tool's purpose, usage, or behavior. While an output schema exists (which might define return values), the description fails to provide essential context for an AI agent to select and invoke the tool correctly, especially compared to numerous sibling tools.

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?

The schema description coverage is 0%, so the description must compensate for undocumented parameters. It adds minimal semantics by specifying that the 'sets' parameter should be 'comma-separated', but does not explain what constitutes a set (e.g., mathematical notation, string format), examples, or constraints. This is inadequate for a tool with one parameter that is fully undocumented in the schema.

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

Purpose2/5

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

The description 'Product of sets (comma-separated)' restates the tool name 'sympy_product_set' in slightly different words, making it tautological. It does not specify what mathematical operation 'product' refers to (e.g., Cartesian product, intersection-like operation) or how it differs from sibling tools like sympy_intersection or sympy_union, leaving the purpose vague.

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

Usage Guidelines1/5

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

No guidance is provided on when to use this tool versus alternatives. With many sibling tools (e.g., sympy_intersection, sympy_union, sympy_complement), the description fails to indicate the specific context or mathematical scenario where this tool is appropriate, offering no usage instructions.

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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