SageMath MCP Server

Geometry Operation

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?

The annotations already convey idempotentHint=true and destructiveHint=false, so the safety profile is mostly covered. The description adds no behavioral context about side effects, session interaction, or error behavior, and readOnlyHint=false is not explained, though it is not contradicted.

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 two sentences with no wasted words: the first fronts the capability set, and the second gives a direct routing instruction. Every sentence contributes useful information.

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?

Combined with a rich schema, output schema, and annotations, the description gives an agent enough to select and invoke the tool correctly. It could add geometric preconditions such as consistent dimension or point-count expectations, but those are minor gaps rather than fatal omissions.

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%, and the schema already documents points, session, and the allowed operation values. The tool description mostly repeats the operation names without adding a meaningful layer of detail about coordinate formats, dimensionality, or minimum point counts.

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?

The description states a clear subject, 'Computational geometry on point sets,' and enumerates five concrete operations: distance, polygon area, polytope volume, convex hull vertices, and convexity tests. This lets an agent know exactly what the tool computes and differentiates it from siblings, especially evaluate_sage.

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?

The description explicitly says to prefer this tool over evaluate_sage for these geometry operations, naming the most likely alternative. It lacks more detailed conditions about when evaluate_sage might still be the better choice, so it falls just short of fully explicit when-not guidance.

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