SageMath MCP Server

find_root

Idempotent

Locate a numeric root of an expression or equation within a specified interval, useful for solving equations numerically when exact solutions are unavailable.

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

B3.3/5.0

Behavior3/5

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

Annotations already declare idempotent=true, destructive=false, and readOnlyHint=false. The description adds that the root is numeric and interval-bound, hinting at approximate/iterative behavior, but does not disclose failure modes, precision, or session side effects. This is modest additional context beyond annotations.

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?

One efficient sentence, front-loaded with the core action and scope. There is no filler or redundancy.

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?

An output schema exists, so return values need not be explained. However, for a tool that overlaps with solve_equation, the description omits routing guidance and assumptions about numeric versus symbolic solving. It is adequate but leaves a notable gap.

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 bounds and session behavior. The description mentions expression/equation and interval but adds no syntax or precision details beyond the schema. Baseline 3 is appropriate when schema does the heavy lifting.

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 ('Find') and resource ('numeric root of an expression or equation') with an interval scope. It is clear on its own, but does not distinguish itself from the sibling solve_equation tool, which likely overlaps in finding solutions.

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?

The description gives no explicit when-to-use guidance, prerequisites, or alternatives. It does not say when to prefer find_root over solve_equation, nor when a numeric root is appropriate versus symbolic solving.

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