SageMath MCP Server

solve_equation

Idempotent

Find exact solutions to single equations or systems of equations for specified variables. Solves symbolically with support for multiple variables and equation lists.

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

C2.9/5.0

Behavior2/5

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

Annotations declare readOnlyHint=false, idempotentHint=true, destructiveHint=false, openWorldHint=false. The description adds no behavioral context beyond these hints—it doesn't explain that solving may return multiple solutions, how the result is structured, or whether the workspace state changes. With annotations covering safety and idempotency, the description should still clarify return semantics, but it is silent.

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 that front-loads the primary action. It is appropriately sized but could be slightly more informative without being verbose.

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 an output schema present, the description need not explain return values. However, given the tool's complexity (systems of equations, multiple variables) and the presence of a related sibling (find_root), the description is minimal. It lacks any contextual hints about typical use cases or limitations, leaving the agent to rely entirely on schema and annotations.

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 parameters are fully documented in the schema. The description adds no additional parameter meaning beyond what the schema already provides. Baseline 3 is appropriate when the schema does all 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 (solve) and resource (equation or system of equations). However, it does not differentiate from sibling find_root, which also solves equations numerically. A mention of the symbolic/exact nature vs find_root would fully distinguish it.

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 tool versus find_root (numeric root finding) or solve_ode (differential equations). An agent must infer that this solves algebraic equations symbolically, but no explicit context or exclusions are given.

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