SageMath MCP Server

series_expansion

Idempotent

Compute Taylor or Laurent series expansions of expressions around a point to approximate functions and analyze local behavior.

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

C2.9/5.0

Behavior2/5

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

Annotations declare idempotentHint=true and destructiveHint=false, but the description adds nothing about behavior: no mention of which workspace/session state is touched, whether the result is returned or stored, or how the expansion interacts with session variables. With openWorldHint=false and readOnlyHint=false, the agent needs clarity the description doesn't provide.

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?

A single front-loaded sentence with zero waste, appropriate for the tool's scope. It is not padded, though it is also not maximally informative per word.

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?

An output schema exists, so return structure needn't be explained. However, for a symbolic math tool with a session/workspace parameter and 5 params, the description leaves the session semantics, point-in-expansion behavior, and the Taylor-vs-Laurent distinction entirely to the schema.

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 coverage is 100%, so every parameter is already documented in the schema, including defaults for order, point, variable, and session. The description adds no parameter-level meaning beyond the schema baseline.

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?

States a specific verb ('Compute') and resource ('Taylor/Laurent series expansion'), clearly distinguishing it from siblings like expand_expression or symbolic_sum. It doesn't need to name a sibling because the math term itself is distinctive.

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 on when to use this vs alternatives such as expand_expression, simplify_expression, or limit_expression, all of which are adjacent symbolic manipulations. An agent must infer the use case from the name alone.

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