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sympy_product_expr

Compute symbolic product expressions by specifying the mathematical expression, variable, and bounds to generate unevaluated Product objects for advanced algebraic analysis.

Instructions

Compute an unevaluated product (Product object).

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
exprYesString expression
variableYesProduct variable
boundsYesLower and upper bound as "lower,upper"

Output Schema

TableJSON Schema
NameRequiredDescriptionDefault
resultYes
Behavior2/5

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

No annotations are provided, so the description carries full burden for behavioral disclosure. It mentions the tool computes an 'unevaluated' product, implying it returns a symbolic representation rather than a numeric result, which is useful. However, it doesn't cover other behavioral aspects like error handling, performance, or output format, leaving significant gaps.

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 a single, efficient sentence that directly states the tool's function without unnecessary words. It's front-loaded with the core action ('Compute'), making it easy to parse, though it could be slightly more informative without losing conciseness.

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

Completeness3/5

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

Given the tool has an output schema (not provided in details but indicated as present), the description doesn't need to explain return values. However, with no annotations and a mathematical operation that might have nuances (e.g., symbolic vs. numeric), the description is minimal but adequate for basic understanding, though it could benefit from more context about the 'unevaluated' aspect.

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 100% description coverage, clearly documenting all three parameters (expr, variable, bounds). The description adds no additional semantic details beyond what the schema provides, such as examples or constraints on the string formats. Baseline 3 is appropriate since the schema does the heavy lifting.

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

Purpose3/5

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

The description states the tool computes an unevaluated product (Product object), which clarifies the verb (compute) and resource (Product object). However, it doesn't distinguish this from sibling tools like 'sympy_product' (which likely evaluates products) or 'sympy_summation' (for sums), leaving the purpose somewhat vague in context.

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?

No guidance is provided on when to use this tool versus alternatives. With many sibling tools for mathematical operations (e.g., 'sympy_product', 'sympy_summation', 'sympy_integrate'), the description lacks any context about when this specific unevaluated product computation 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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