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series_expansion

Compute a Taylor or Laurent series expansion of an expression at a given point, with control over variable and number of terms.

Instructions

Compute a Taylor/Laurent series expansion

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
orderNoNumber of terms in the expansion
pointNoPoint around which to expand0
sessionNoNamed workspace to use. Workspaces have independent variables; omit for 'default'.default
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 behavioral disclosure. It only states the operation, with no mention of default order/point, session handling, output format, or limitations, which is insufficient for a tool with 5 parameters.

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 single-sentence description is very concise and free of fluff, but it is minimal to the point of under-specification. It earns its place by stating the core purpose, though it could include more useful context without becoming bloated.

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 the 5 parameters, lack of annotations, and many sibling tools, the description is too sparse. It relies entirely on the schema for parameter understanding and provides no context about when series expansion is appropriate or how it differs from related operations. The output schema exists, but the description does not leverage it.

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 provides descriptions for all 5 parameters with defaults and examples, achieving 100% coverage. The description adds no parameter-specific information, so the baseline score of 3 applies.

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 computes a Taylor/Laurent series expansion, using a specific verb and resource. It distinguishes from siblings like expand_expression, though it does not explicitly name alternatives.

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 such as expand_expression or limit_expression. There are no exclusions, prerequisites, or typical use cases mentioned.

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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