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SageMath MCP Server

by XBP-Europe
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Python
Hybrid

Plot Multi Expression

plot_multi_expression
Idempotent

Plot multiple mathematical expressions on a single 2D graph to visually compare their behavior, returning a rendered image.

Instructions

Plot multiple expressions overlaid on a single 2D graph, as a rendered image

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
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
variableNoPlot variablex
range_maxNoUpper bound of plot range
range_minNoLower bound of plot range
expressionsYesList of expressions to plot (e.g. ['sin(x)', 'cos(x)'])
image_formatNoImage format to return: 'png' (raster) or 'svg' (vector, smaller)png

Schema Changelog

Changes observed during successful MCP inspections.

  1. Changed3 schema fields changedv0.7.0
    • addedInput schema / properties / image_format
      Added value: +{
+  "default": "png",
+  "description": "Image format to return: 'png' (raster) or 'svg' (vector, smaller)",
+  "enum": [
+    "png",
+    "svg"
+  ],
+  "type": "string"
+}
    • 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'."
    • changedOutput schema / (root)
      Previous value: -{
-  "additionalProperties": true,
-  "type": "object"
-}New value: +null
  2. Changed1 schema field 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"
+}
  3. First observedv0.3.1

TDQS

A4/5.0
Behavior4/5

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

The description adds context beyond annotations by stating the output is a rendered image and that expressions are overlaid on a single graph. Annotations already indicate idempotency and non-destructiveness, but the output format is a valuable addition not covered by annotations.

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 a single, efficient sentence that front-loads the core purpose and output. No wasted words; it conveys the essential information without redundancy.

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 plotting tool with full schema coverage, the description adequately covers the high-level behavior, output type, and the overlay aspect. It does not mention any caveats or additional details, but given the schema's completeness, the description is sufficient for an agent to call the tool correctly.

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 each parameter is already documented. The description adds minimal semantic value beyond the schema, mainly reinforcing that multiple expressions are plotted. It does not clarify parameter formats or constraints beyond what the schema provides.

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 clearly states a specific verb ('Plot'), resource ('multiple expressions'), and output ('a rendered image') on a single 2D graph. It differentiates from siblings like plot_expression (single) and plot3d_expression (3D) through the phrase 'multiple expressions overlaid' and '2D'.

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 description implies usage for multiple expressions but does not explicitly state when to use this tool versus alternatives like plot_expression or plot3d_expression. No exclusions or explicit conditions are provided; the guidance is only implicit through the tool name and description.

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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