SageMath MCP Server

limit_expression

Idempotent

Compute the limit of a mathematical expression as a variable approaches a given point, optionally specifying left or right direction. Use for symbolic calculus and asymptotic analysis.

Instructions

Compute the limit of an expression

Input Schema

TableJSON Schema

Name	Required	Description	Default
`point`	No	Point to approach (e.g., '0', 'oo', '-oo')	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 approaching the point	x
`direction`	No	Direction: 'plus' (right), 'minus' (left), or omit for both
`expression`	Yes	Expression to take the limit of

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

C2.4/5.0

Behavior2/5

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

Annotations already state readOnlyHint=false, idempotentHint=true, destructiveHint=false, and openWorldHint=false. The description adds no behavioral context, such as why the operation is not read-only (likely because it mutates the session workspace) or how the workspace is affected. It neither contradicts nor enriches the annotations.

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 description is a single front-loaded sentence with no filler or repetition. It is appropriately terse, though it leaves many details to the schema and annotations.

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 tool's complexity (five parameters including a session bearer credential, an output schema, and many sibling math tools), the description is too sparse. It does not mention session/workspace management or when this tool is preferred over related operations, leaving the agent to rely entirely on the schema and name.

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%, so the schema thoroughly documents all five parameters including defaults and the session token. The description adds no parameter semantics beyond what the schema already provides. The baseline of 3 applies.

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 restates the tool name ('limit_expression' → 'Compute the limit of an expression') without adding scope, constraints, or distinguishing features from sibling calculus tools like differentiate_expression or integrate_expression. It identifies the verb and resource but provides no selection value.

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 given on when to use this tool versus alternatives, no prerequisites are stated, and the session/workspace context is ignored. The agent must infer usage entirely from the name and schema.

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