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SageMath MCP Server

by XBP-Europe
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Python
Hybrid

Plot3D Expression

plot3d_expression
Idempotent

Plot a 3D surface from a two-variable math expression, returning a rendered PNG or SVG image.

Instructions

Plot a 3D surface of a two-variable expression 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
expressionYesExpression of two variables (e.g. 'sin(x)*cos(y)')
x_variableNoFirst variablex
y_variableNoSecond variabley
x_range_maxNoX upper bound
x_range_minNoX lower bound
y_range_maxNoY upper bound
y_range_minNoY lower bound
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

B3.3/5.0
Behavior2/5

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

Annotations already indicate idempotentHint=true, destructiveHint=false, but the description adds no behavioral context beyond stating that it produces a rendered image. It does not explain any side effects, session state implications, or failure modes, relying entirely on the annotations for safety signals.

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, front-loaded sentence with no filler. It efficiently captures the action, resource, and output format.

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?

With 9 parameters and no output schema, the description gives the essential purpose and output type ('rendered image'), but does not address session behavior or how the image is returned (e.g., data URL, file). It is adequate for a simple plotting tool but leaves some operational detail unspecified.

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?

The input schema covers all 9 parameters with descriptions, so the baseline is 3. The description itself does not add any parameter-level meaning, but it does not need to because the schema handles that burden.

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 'Plot a 3D surface of a two-variable expression as a rendered image' uses a specific verb and resource, and clearly distinguishes from siblings like plot_expression (2D) and plot_multi_expression (multiple expressions). An agent can immediately tell this is for 3D surface plots of a single two-variable expression.

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?

The description provides no guidance on when to use this tool versus alternatives such as plot_expression or plot_multi_expression, and does not mention any exclusions or prerequisites. An agent is left to infer usage from the name and schema alone.

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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