SageMath MCP Server

group_operation

Idempotent

Compute group properties (order, is_abelian, center_order) for a given Sage group by specifying the operation. Returns the requested group theory result.

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

A3.6/5.0

Behavior3/5

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

Annotations declare readOnlyHint=false, idempotentHint=true, destructiveHint=false. The description corroborates the non-read-only nature by saying it 'constructs' groups, which plausibly mutates session/workspace state, but it never says whether constructed groups persist in the workspace, whether they consume named slots, or what happens on repeated calls. Given the annotation coverage, this is an acceptable but thin addition.

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 compact sentence with the domain front-loaded and the capability list immediately following. No filler, no restatement of the tool name.

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?

An output schema exists, so return-value documentation is not required, and all three parameters are richly described in the schema. What remains under-covered is behavioral: whether the group construction is ephemeral or persisted into the named session, and how a previously constructed group is referenced in later calls. For a simple constructor+query tool this is close to complete, but that persistence question is non-trivial.

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 group, session, and operation are already fully documented (including the session bearer-credential warning). The description's list of operations ('order, is_abelian, center, etc.') only loosely restates the schema's exact enumeration ('center_order', 'conjugacy_classes_count'), adding no syntax or semantics beyond the schema. Baseline 3 per the rules.

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 concrete verb set ('construct groups and query properties') and the domain resource (group theory), with example properties (order, is_abelian, center). The domain naming clearly separates it from sibling operations like number_theory_operation, combinatorics_operation, or graph_operation. It falls short of 5 only because 'construct groups' leaves ambiguous what happens to the constructed object (is it stored, named, returned?).

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?

Usage is implied by the domain: an agent can infer that this tool is for group-theoretic questions rather than polynomial or number-theory ones. However, there is no explicit when-to-use guidance, no mention of prerequisites (e.g., needing a session/workspace), and no statement of which sibling operations overlap or when to prefer evaluate_sage instead.

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