SageMath MCP Server

Series Expansion

series_expansion

Idempotent

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

Instructions

Compute a Taylor/Laurent series expansion

Input Schema

TableJSON Schema

Name	Required	Description	Default
`order`	No	Number of terms in the expansion
`point`	No	Point around which to expand	0
`session`	No	Workspace to use, as a name or a portable handle. Workspaces have independent variables. A name is scoped to this MCP session; a handle returned by start_sage_session (workspace_token) reaches the same workspace across reconnects and is a bearer credential -- keep it secret. Omit for 'default'.	default
`variable`	No	Variable for expansion	x
`expression`	Yes	Expression to expand in series

Output Schema

TableJSON Schema

Name	Required	Description	Default
No arguments

Schema Changelog

Changes observed during successful MCP inspections.

Changed1 schema field changedv0.7.0Sep 12, 2026

changedInput schema / properties / session / description

Previous value: -"Named workspace to use. Workspaces have independent variables; omit for 'default'."New value: +"Workspace to use, as a name or a portable handle. Workspaces have independent variables. A name is scoped to this MCP session; a handle returned by start_sage_session (workspace_token) reaches the same workspace across reconnects and is a bearer credential -- keep it secret. Omit for 'default'."

Changed1 schema field changedv0.5.0Aug 14, 2026

addedInput schema / properties / session

Added value: +{
+  "default": "default",
+  "description": "Named workspace to use. Workspaces have independent variables; omit for 'default'.",
+  "type": "string"
+}

First observedv0.3.1Jul 31, 2026

TDQS

A3.5/5.0

Behavior2/5

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

The description adds no behavioral traits beyond the annotations. Annotations provide idempotentHint=true and destructiveHint=false, but the description does not explain side effects, error handling, return details, or limitations (e.g., singularities, convergence). It does not contradict the annotations, but also adds no 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?

A single sentence that front-loads the core purpose with no filler or redundancy. Every word earns its place, making it highly efficient.

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?

The schema fully documents parameters and an output schema exists, so basic invocation is well-covered. However, the description omits guidance on differentiating from expansion-like siblings and provides no behavioral or usage context, making it only partially complete.

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?

Schema description coverage is 100%, with all five parameters (order, point, session, variable, expression) documented in the input schema. The description adds no additional parameter semantics, 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.

Purpose5/5

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

The description uses a specific verb ('Compute') and identifies the exact resource ('a Taylor/Laurent series expansion'). This clearly distinguishes it from sibling tools like expand_expression or simplify_expression, which handle algebraic expansion rather than power-series expansions.

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 usage: an agent can infer this tool is for Taylor/Laurent series expansions. However, it provides no explicit guidance about when to prefer this over expand_expression or other series-related siblings, nor any exclusions or alternatives.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.