SageMath MCP Server

differentiate_expression

Idempotent

Compute symbolic derivatives of a mathematical expression with respect to a chosen variable, including higher-order derivatives.

Instructions

Differentiate an expression with respect to a variable

Input Schema

TableJSON Schema

Name	Required	Description	Default
`order`	No	Order of differentiation (1 = first, 2 = second, etc.)
`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 differentiation	x
`expression`	Yes	Expression to differentiate

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 cover the safety profile (non-destructive, idempotent, not read-only), but the description adds nothing beyond them. It says nothing about how the session/workspace state is affected, which is notable given readOnlyHint=false and the workspace-scoping semantics documented only in the schema.

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 efficient sentence with the verb and resource front-loaded and no wasted words. It is arguably under-specified rather than over-long, but structurally clean.

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 values need not be described, and the schema fully documents parameters. However, for a non-read-only symbolic operation with session-scoped state, the description is thin on behavior and use context.

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 all four parameters (expression, variable, order, session) are already documented in the schema, including the order default and workspace/bearer-credential nuances. The description adds no parameter detail beyond that, which is the expected baseline when the schema does the work.

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 (differentiate) and resource (expression) with the scope qualifier 'with respect to a variable'. It is distinguishable from siblings like integrate_expression or limit_expression, though it never names them explicitly.

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 versus integrate_expression or other symbolic tools, and no prerequisites mentioned. The only context is the scope qualifier 'with respect to a variable', which is implied usage at best.

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