SageMath MCP Server

Limit Expression

limit_expression

Idempotent

Compute the limit of a mathematical expression as a variable approaches a specified point, with optional one-sided direction.

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

C2.9/5.0

Behavior2/5

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

The annotations (idempotentHint=true, readOnlyHint=false, destructiveHint=false) carry the safety profile, but the description adds no behavioral context beyond them. It doesn't disclose that computation occurs in a Sage workspace, that results may be undefined or symbolic, or that the 'session' parameter implies stateful behavior — all of which would be valuable context for a computational tool.

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 six-word sentence with zero filler and the key action front-loaded. It is appropriately terse, though arguably so minimal that it borders on under-specification for a tool with five parameters.

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?

With 100% schema coverage, an output schema, and informative annotations, the structured data carries most of the load. The description is complete for stating the core purpose, but lacks usage context such as when a limit is appropriate versus a series expansion or direct evaluation, and gives no hint of the tool's limitations for a math-computation context with many siblings.

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 fully documents all five parameters including defaults and the session credential warning. The description adds no parameter-level detail, but the baseline of 3 applies because the schema does the heavy lifting.

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 states a specific verb ('Compute') and resource ('the limit of an expression'), which clearly identifies the mathematical operation. It is distinguishable from siblings like differentiate_expression and integrate_expression primarily through the tool name rather than the description text itself, but the purpose is unambiguous.

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?

The description provides zero guidance on when to use this tool versus alternatives. There is no mention of when a limit is the right operation versus series_expansion, solve_equation, or evaluate_sage, and no exclusions or prerequisites are stated.

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