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sympy_dirichlet_eta

Compute the Dirichlet eta function for symbolic mathematics. Use this tool to evaluate eta(s) values for complex analysis and number theory calculations.

Instructions

Dirichlet eta function.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
sYes

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. The description reveals nothing about what the tool actually does - whether it computes values, returns symbolic expressions, handles special cases, or has any behavioral characteristics. For a mathematical function tool with zero annotation coverage, this complete lack of behavioral information is inadequate.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness3/5

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is extremely concise (two words) but this brevity comes at the cost of being under-specified rather than efficiently informative. While it's front-loaded with the only information provided, the single phrase doesn't earn its place by adding meaningful value beyond the tool name.

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 function tool with no annotations, 0% schema description coverage, but with an output schema present, the description is incomplete. While the output schema may document return values, the description should still explain what operation the tool performs on the Dirichlet eta function. For a tool in a complex mathematical library with many similar functions, more context is needed about its specific purpose and behavior.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters1/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

The schema description coverage is 0%, meaning the parameter 's' is completely undocumented in the schema. The description provides no information about what 's' represents (presumably a complex variable or expression), its expected format, valid ranges, or how it's used. With one required parameter and no schema documentation, the description fails to compensate for this gap.

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 'Dirichlet eta function.' is a tautology that restates the tool name without specifying what the tool does. It doesn't indicate whether this computes, evaluates, simplifies, or performs some other operation on the Dirichlet eta function. Compared to sibling tools like 'sympy_evalf' (evaluates numerically) or 'sympy_simplify' (simplifies expressions), this description fails to distinguish the tool's specific function.

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 no guidance on when to use this tool versus alternatives. With many sibling tools for mathematical functions (e.g., sympy_zeta, sympy_gamma), there's no indication of what problem this tool solves or when it should be selected. The description doesn't mention prerequisites, typical use cases, or relationships to other mathematical functions.

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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