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sympy_limit

Compute mathematical limits of expressions as variables approach specific points, including directional limits from left or right.

Instructions

Compute a limit.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
exprYesString expression
variableYesVariable approaching the limit
pointYesPoint to approach
directionNoDirection ("+", "-")+

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 carries the full burden of behavioral disclosure. 'Compute a limit.' reveals nothing about the tool's behavior: no information about computational complexity, error handling, symbolic vs numeric computation, domain restrictions, or what happens with undefined limits. For a mathematical tool with no annotation coverage, this description is completely inadequate for understanding how the tool behaves.

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 maximally concise with just three words. While this represents severe under-specification, from a pure conciseness perspective it's efficient with zero wasted words. The structure is simple and direct, though this comes at the cost of meaningful content.

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 that this is a mathematical computation tool with no annotations, 4 parameters, and an output schema (though we don't see its content), the description is severely incomplete. 'Compute a limit.' doesn't explain what mathematical limits are computed, what format the expression should be in, how to handle special cases like infinity, or what the tool returns. While the output schema might document return values, the description fails to provide essential context for proper tool selection and use.

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, with all four parameters (expr, variable, point, direction) clearly documented in the schema. The description adds zero additional information about parameter semantics, usage patterns, or examples. However, since schema coverage is high, the baseline score of 3 is appropriate - the schema does the heavy lifting while the description adds no value.

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 'Compute a limit.' is a tautology that essentially restates the tool name 'sympy_limit'. While it correctly identifies the mathematical operation, it doesn't specify what kind of limit (mathematical limit of an expression) or distinguish this from sibling tools that perform other mathematical operations like integration, differentiation, or simplification. It provides minimal value beyond the tool name itself.

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?

The description provides absolutely no guidance about when to use this tool versus alternatives. With 100+ sibling tools in the SymPy family, there's no indication of when limit computation is appropriate versus using sympy_derivative, sympy_integrate, sympy_solve, or other mathematical operations. The description offers no context about prerequisites, mathematical domains, or typical use cases.

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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