SageMath MCP Server

Solve Ode

solve_ode

Idempotent

Solve ordinary differential equations of any order and obtain the general solution with arbitrary constants.

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 disclose idempotency and non-destructive behavior. The description adds that it returns a general solution with arbitrary constants, which is useful but not extensive. It does not mention any side effects or workspace-specific behavior beyond what the schema already covers.

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?

Two concise sentences with no fluff. The core purpose is stated first, followed by a clear usage hint. Every word earns its place.

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?

Given the output schema and full schema descriptions, the description provides sufficient context for an agent to call the tool correctly. It clarifies the return type and gives a usage preference. It could be more exhaustive about edge cases (e.g., initial conditions) but is adequate for its complexity.

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% with detailed descriptions for all parameters. The description does not add any parameter-specific meaning beyond the schema, so the baseline score of 3 is appropriate.

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?

States a specific verb (solve), a specific resource (ordinary differential equation), and a clear outcome (general solution with arbitrary constants). It also explicitly differentiates itself from evaluate_sage, making its purpose unambiguous.

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?

Provides an explicit preference for this tool over evaluate_sage, which is a direct usage guideline. However, it does not mention when not to use it or other sibling alternatives like solve_equation, so it lacks full coverage of exclusions.

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