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SageMath MCP Server

by XBP-Europe
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Python
Hybrid

plot_multi_expression

Idempotent

Overlay multiple mathematical expressions on a single 2D graph and render them as a PNG or SVG image for comparison.

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

A3.6/5.0
Behavior3/5

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

Annotations already declare destructiveHint=false, idempotentHint=true, and openWorldHint=false, so the safety profile is covered. The description adds the return medium ('as a rendered image'), which is useful because there is no output schema, but says nothing about how the image is delivered, size limits, or rendering cost. Note readOnlyHint=false is set even though plotting mutates nothing, but the description makes no conflicting claim, so this is not a contradiction.

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?

A single front-loaded sentence with no filler; the distinguishing qualifier ('multiple', 'single 2D graph') comes before the output form.

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?

With no output schema, stating that the result is a rendered image is the key missing piece and it is present. The remaining gaps (how the image is returned in the response, session/workspace expectations) are covered by the schema or are minor for a plotting tool.

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 all six parameters (session, variable, range_min/max, expressions, image_format) are already documented in the schema. The description's 'multiple expressions' merely echoes the expressions array and adds no format, default, or range semantics. Baseline 3 applies when the schema does the heavy lifting.

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 gives a specific verb (plot), a specific resource (multiple expressions), and the exact output form (overlaid on a single 2D graph, rendered image). The words 'multiple' and '2D' inherently separate it from the sibling plot_expression (single) and plot3d_expression (3D), so an agent can route to it from names alone.

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?

There is no explicit when-to-use, when-not-to-use, or named alternative. An agent must infer from 'multiple expressions' that single-expression plotting belongs to plot_expression, and nothing addresses 3D cases or session prerequisites. Implied routing only, with no stated conditions.

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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