SageMath MCP Server

Find Root

find_root

Idempotent

Locate a numeric root of an equation or expression within a given interval.

Instructions

Find a numeric root of an expression or equation in a given interval

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
`variable`	No	Variable	x
`expression`	Yes	Expression or equation to find a root of (e.g. 'x - cos(x)', or 'E - 0.6*sin(E) = 0.75')
`lower_bound`	No	Left bound of search interval
`upper_bound`	No	Right bound of search interval

Output Schema

TableJSON Schema

Name	Required	Description	Default
No arguments

Schema Changelog

Changes observed during successful MCP inspections.

Changed2 schema fields changedv0.7.0Sep 12, 2026

changedInput schema / properties / expression / description

Previous value: -"Expression to find root of (e.g. 'x - cos(x)')"New value: +"Expression or equation to find a root of (e.g. 'x - cos(x)', or 'E - 0.6*sin(E) = 0.75')"

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

A3.6/5.0

Behavior3/5

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

Annotations already declare idempotentHint=true and destructiveHint=false, covering safety and repeatability. The description adds only the 'numeric' qualifier, which signals approximate rather than symbolic behavior, but does not disclose algorithm behavior, no-root outcomes, or potential caveats.

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?

The description is a single efficient sentence with no filler. It front-loads the core operation ('find a numeric root') and includes the essential scope ('in a given interval') without waste.

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 rich input schema, presence of an output schema, and annotations, the description is largely sufficient for an agent to invoke the tool correctly. The main gap is the lack of explicit routing guidance versus solve_equation, but that is a minor omission here.

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 the schema already documents all five parameters including the expression format and bounds. The description reinforces the domain but does not add meaning beyond what the parameter descriptions already provide.

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 clearly states a specific operation: find a numeric root of an expression or equation within a given interval. It is unambiguous about the resource and action, though it does not explicitly distinguish itself from the sibling solve_equation tool.

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 phrase 'numeric root... in a given interval' implies this tool is for numerical interval-based root finding, which hints at when it should be used versus symbolic solving. However, it does not explicitly name alternatives or state when not to use it.

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