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XBP-Europe

SageMath MCP Server

by XBP-Europe
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Python
Hybrid

graph_operation

Idempotent

Create named or custom graphs and compute graph properties such as chromatic number, connectivity, diameter, order, size, degree sequence, adjacency matrix, or shortest path.

Instructions

Graph theory: create named graphs and compute properties (chromatic_number, is_connected, diameter, etc.)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
graphYesGraph constructor: a named graph like 'PetersenGraph' or an adjacency dict like '{0:[1,2], 1:[0,2], 2:[0,1]}'
sourceNoSource vertex
targetNoTarget vertex
sessionNoWorkspace 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
operationYesOne of: chromatic_number, is_connected, is_planar, diameter, order, size, degree_sequence, adjacency_matrix, shortest_path (requires source and target)

Output Schema

TableJSON Schema
NameRequiredDescriptionDefault

No arguments

Schema Changelog

Changes observed during successful MCP inspections.

  1. Changed1 schema field changedv0.7.0
    • 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'."
  2. Changed3 schema fields changedv0.5.0
    • addedInput schema / properties / session
      Added value: +{
+  "default": "default",
+  "description": "Named workspace to use. Workspaces have independent variables; omit for 'default'.",
+  "type": "string"
+}
    • changedInput schema / properties / source / anyOf
      Previous value: -[
-  {
-    "type": "integer"
-  },
-  {
-    "type": "null"
-  }
-]New value: +[
+  {
+    "type": "integer"
+  },
+  {
+    "type": "string"
+  },
+  {
+    "type": "null"
+  }
+]
    • changedInput schema / properties / target / anyOf
      Previous value: -[
-  {
-    "type": "integer"
-  },
-  {
-    "type": "null"
-  }
-]New value: +[
+  {
+    "type": "integer"
+  },
+  {
+    "type": "string"
+  },
+  {
+    "type": "null"
+  }
+]
  3. First observedv0.3.1

TDQS

B3.2/5.0
Behavior3/5

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

Annotations already declare readOnlyHint=false, idempotentHint=true, and destructiveHint=false, conveying the safety/mutation profile. The description adds that graphs are named and created within a session, but says nothing about state persistence, workspace scoping, or side effects beyond what annotations and the session param provide.

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?

A single compact sentence with the core purpose front-loaded and no wasted words. It is efficient, though the parenthetical operation list is partly redundant with the schema.

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 described, and the schema is fully documented. However, a multi-operation dispatcher tool benefits from stating when to pick which operation, and the description omits that routing context.

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 graph, source, target, session, and operation comprehensively, including the shortest_path prerequisite. The description adds no parameter meaning beyond restating a few operation names, so the baseline 3 applies.

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+resource combination: 'create named graphs' and 'compute properties,' naming concrete operations like chromatic_number and diameter. It is clear this is a graph-theory dispatcher, though it doesn't contrast itself against a hypothetical graph sibling.

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?

No guidance on when to use this tool versus alternatives, nor prerequisites (e.g., that shortest_path requires source and target, which only appears buried in the operation enum). The agent must infer usage entirely from the schema.

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

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