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XBP-Europe
by XBP-Europe

series_expansion

Compute Taylor or Laurent series expansions of mathematical expressions around a given point, specifying the variable and number of terms for precise symbolic approximation.

Instructions

Compute a Taylor/Laurent series expansion

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
orderNoNumber of terms in the expansion
pointNoPoint around which to expand0
variableNoVariable for expansionx
expressionYesExpression to expand in series

Output Schema

TableJSON Schema
NameRequiredDescriptionDefault

No arguments

Behavior2/5

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

With no annotations provided, the description carries the full burden of disclosing behavioral traits. It only says 'Compute a Taylor/Laurent series expansion' and does not mention output format, mutability/side effects, edge cases, or how Taylor vs Laurent is determined. This is a significant transparency gap for an unannotated tool.

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 a single, front-loaded sentence that communicates the tool's purpose with zero wasted words. It is concise and immediately understandable.

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

Completeness4/5

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

The schema fully documents parameters and an output schema exists, so the overall tool definition is largely complete. The description, while minimal, is specific enough for an agent to select the tool when a series expansion is needed, though it lacks usage guidance and deeper behavioral context.

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 schema description coverage is 100%, so all four parameters are already described with details like defaults and purpose. The description adds no additional parameter-level meaning, earning the baseline score of 3.

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

Purpose5/5

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

The description 'Compute a Taylor/Laurent series expansion' uses a specific verb and resource, clearly distinguishing it from sibling tools like expand_expression or limit_expression. It precisely conveys the core operation of the tool.

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

Usage Guidelines3/5

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

The description implies the tool is for computing series expansions, but it provides no explicit guidance on when to prefer it over alternatives or when not to use it. There are no exclusions or comparisons with sibling tools, leaving usage context only implied.

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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