SageMath MCP Server

solve_ode

Idempotent

Solve any ordinary differential equation and return its general solution with arbitrary constants. Use this instead of a general evaluator for ODE problems.

Instructions

Solve an ordinary differential equation of any order, returning the general solution with arbitrary constants. Prefer this over evaluate_sage.

Input Schema

TableJSON Schema

Name	Required	Description	Default
`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
`equation`	Yes	ODE string, e.g., "diff(y(x),x) + y(x) = 0"
`function`	No	Dependent function name (e.g., 'y')	y
`variable`	No	Independent variable (e.g., 'x')	x

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

A4/5.0

Behavior3/5

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

Annotations already declare idempotentHint=true, readOnlyHint=false, destructiveHint=false and openWorldHint=false. The description adds that the return is a general solution with arbitrary constants, which is behavioral context beyond annotations. But it doesn't note that this may execute in a persistent session/workspace that affects state across calls (as strongly implied by the 'session' parameter).

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 efficient sentence with the highest-value routing hint ('Prefer this over evaluate_sage') placed at the end. No filler.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness4/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Has an output schema, so return values need not be explained, and the equation format is shown in the schema. Routing to evaluate_sage covers the main sibling-confusion risk. Slightly incomplete on session workspace interactions, but overall fit for purpose.

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 parameters are fully documented in the schema (session/workspace semantics, equation format example, function name, variable name). The description adds nothing beyond the schema about parameters; baseline 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?

Specific verb (Solve) + resource (ordinary differential equation of any order) + output shape (general solution with arbitrary constants). Distinguishes clearly from siblings like solve_equation (algebraic) and evaluate_sage.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines4/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

Explicitly says 'Prefer this over evaluate_sage', giving one clear alternative routing rule. However, it doesn't address when to use solve_equation (algebraic equations) vs this ODE solver, nor prerequisites for the session workspace handling.

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