SageMath MCP Server

statistics_summary

Idempotent

Compute mean, median, variance, standard deviation, min, and max for a list of numbers using SageMath, replacing generic symbolic evaluation for descriptive statistics.

Instructions

Descriptive statistics for a list of numbers: mean, median, population and sample variance and standard deviation, min and max. Prefer this over evaluate_sage for summary statistics.

Input Schema

TableJSON Schema

Name	Required	Description	Default
`data`	Yes	List of numeric values
`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

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

A4/5.0

Behavior3/5

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

Annotations are present (readOnlyHint=false, idempotentHint=true, destructiveHint=false), which carry the safety profile, so the description is not required to restate them. However, the description adds no behavioral context at all: it does not mention the session/workspace side effects implied by readOnlyHint=false, nor ordering, empty-list handling, or numeric tolerance. Adequate given annotations, but no added value.

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?

Two sentences, zero waste, and the core capability is front-loaded ahead of the routing hint. Every clause earns its place by naming a returnable statistic or a sibling.

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 formatting need not be explained, and the enumerated statistics cover the semantic surface. The only gap is the absence of any note on the session/workspace interaction implied by readOnlyHint=false, though the schema parameter description partially covers it.

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%: both `data` (list of numbers) and `session` (workspace name/handle, secret handling, default behavior) are fully documented in the schema. The description adds nothing about parameters, so the baseline 3 applies.

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?

Names a specific operation (descriptive statistics) and enumerates exactly which statistics it returns (mean, median, population/sample variance and standard deviation, min, max), so the agent knows precisely what it computes. It also distinguishes itself from the sibling evaluate_sage, which is the closest ambiguous alternative.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines4/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

Explicitly states the preference condition: 'Prefer this over evaluate_sage for summary statistics.' That is a clear routing rule with a named alternative. It does not state when-not to use this tool (e.g., single-value or symbolic cases), so it falls short of the top score.

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