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sympy_arg

Calculate the argument (phase angle) of complex numbers using symbolic mathematics to analyze complex number properties in mathematical computations.

Instructions

Argument of complex number.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
exprYes

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 the full burden of behavioral disclosure. It states the mathematical operation but doesn't describe key behaviors: whether the input expression is evaluated, how errors are handled (e.g., for non-complex inputs), the output format (though an output schema exists), or computational characteristics. For a tool with zero annotation coverage, this is a significant gap in transparency.

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—a single, direct phrase—with no wasted words. It is front-loaded and efficiently communicates the core function without unnecessary elaboration, making it easy to parse quickly.

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's low complexity (single parameter, mathematical function) and the presence of an output schema (which handles return values), the description is minimally complete. However, it lacks context on usage, behavioral details, and parameter guidance, which are gaps despite the structured support. For a tool with no annotations and low schema coverage, it should do more to compensate.

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 description adds no parameter semantics beyond the input schema, which has 0% description coverage. It doesn't explain what 'expr' should contain (e.g., a complex number expression in SymPy syntax) or provide examples. However, with only one parameter and an output schema likely defining the result, the baseline is 3 as the schema provides minimal structure, but the description fails to compensate for the lack of schema documentation.

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: computing the argument of a complex number. It uses a specific mathematical term ('argument') and identifies the resource ('complex number'), making the function unambiguous. However, it doesn't explicitly differentiate from siblings like 'sympy_re' (real part) or 'sympy_im' (imaginary part), which are related but distinct operations on complex numbers.

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 doesn't mention prerequisites (e.g., input must be a complex number), contrast with sibling tools (e.g., 'sympy_abs' for magnitude), or specify typical use cases (e.g., phase angle calculations). This leaves the agent without context for tool selection.

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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