SageMath MCP Server

Group Operation

group_operation

Idempotent

Construct groups from standard SageMath constructors and retrieve key algebraic properties including order, abelianness, cyclicity, center size, conjugacy classes, and exponent.

Instructions

Group theory: construct groups and query properties (order, is_abelian, center, etc.)

Input Schema

TableJSON Schema

Name	Required	Description	Default
`group`	Yes	Sage group constructor, e.g. 'SymmetricGroup(5)', 'DihedralGroup(4)', 'CyclicPermutationGroup(6)', 'AlternatingGroup(5)'
`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: order, is_abelian, is_cyclic, center_order, conjugacy_classes_count, exponent

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

A3.5/5.0

Behavior3/5

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

Annotations already convey idempotence and non-destructiveness; the description adds the construction/query framing but does not disclose whether constructed groups persist in the session or how workspace state is affected. The session parameter documentation covers workspace mechanics, but the description itself does not.

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?

One short, front-loaded sentence with no wasted words. It is concise, though slightly vague around 'construct groups' versus query-only operations.

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?

The input schema and output schema carry the detailed group constructors, operation values, and session semantics, so the description only needs to orient the agent. The main missing nuance is how invalid constructors or session-specific evaluation errors are handled, which is minor.

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 coverage is 100%, so the baseline is 3; the description merely echoes operation examples and adds no new parameter meaning. The parenthetical 'center' is also a loose shorthand for the valid 'center_order' value, a small accuracy risk.

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 anchors the tool in group theory and names concrete query properties, so an agent can distinguish it from calculus, polynomial, or graph siblings. It is not a tautology, but 'construct groups and query properties' is slightly broader than the actual operation list, which only queries group properties.

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 'Group theory:' provides an implied domain, but the description never states when to prefer this tool over siblings like number_theory_operation or combinatorics_operation, nor does it give exclusions. It relies on the tool name and domain label to route the agent.

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