SageMath MCP Server

geometry_operation

Idempotent

Compute geometric properties of point sets: euclidean distance, polygon area, polytope volume, convex hull vertices, and convexity tests.

Instructions

Computational geometry on point sets: euclidean distance, polygon area, polytope volume, convex hull vertices and convexity tests. Prefer this over evaluate_sage for these.

Input Schema

TableJSON Schema

Name	Required	Description	Default
`points`	Yes	List of points as coordinate lists
`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
`operation`	Yes	One of: distance, polygon_area, polytope_volume, convex_hull_vertices, is_convex

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 cover the safety profile (readOnlyHint=false, idempotentHint=true, destructiveHint=false), so the bar is lower. The description adds no behavioral context about computation cost, numerical precision, or what the output contains. It doesn't contradict annotations, but adds little beyond them.

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 sentences, front-loaded with the core purpose and operation list, with the alternative routing as a compact second sentence. No 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?

For a read-only computational tool with full schema coverage and an output schema, the description provides adequate context. Missing only minor details like expected output format or edge-case behavior, but nothing critical for correct invocation.

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 (points, session, operation) are documented in the schema. The description mentions 'point sets' which implies the points parameter, but adds no syntax, format, or constraint details beyond the schema. Baseline 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+resource (computational geometry on point sets) and enumerates the exact operations (euclidean distance, polygon area, polytope volume, convex hull vertices, convexity tests). This clearly distinguishes it from the broad evaluate_sage sibling.

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?

Explicitly names the preferred alternative: 'Prefer this over evaluate_sage for these.' However, it doesn't state when NOT to use it (e.g., for operations not in the list) or point to other geometry-specific siblings, leaving some inference to the agent.

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