SageMath MCP Server

Solve Equation

solve_equation

Idempotent

Solve a single equation or a system of equations for specified variables, returning exact symbolic solutions.

Instructions

Solve an equation or system of equations

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	Equation string (e.g., 'x^2 - 1 = 0') or list of equations for systems
`variable`	No	Variable or list of variables to solve for	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

B3.4/5.0

Behavior2/5

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

Annotations already communicate idempotence and non-destructiveness, but the description itself adds no behavioral context. It does not mention session-related state, possible lack of closed-form solutions, or whether the operation can be expensive.

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, front-loaded sentence that wastes no words and usefully extends the title from 'equation' to 'system of equations.' Every part of the sentence 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?

With a fully documented schema, side-effect annotations, and an output schema present, the main missing element is guidance on scope boundaries versus related equation-solving tools. For a straightforward solve utility, the definition is nearly complete, though not exemplary.

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?

The input schema covers all three parameters with 100% coverage, including defaults, the list form for systems, and the session/workspace semantics, so the baseline of 3 applies. The description contributes no parameter-level meaning beyond what the schema already establishes.

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 the exact action ('solve') and resource ('equation or system of equations'), so an agent can tell what the tool does. It stops short of explicitly distinguishing itself from siblings like solve_ode and find_root, so it misses the sibling-differentiation tier.

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

Usage Guidelines3/5

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

The description implies when to use the tool: whenever an equation or system needs solving. However, it gives no explicit guidance about alternatives, such as preferring solve_ode for differential equations or find_root for scalar root-finding, and includes no exclusions.

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