SageMath MCP Server

distribution_operation

Idempotent

Evaluate probability distributions: compute PDF, CDF, quantile, mean, variance, or generate samples for normal, exponential, Poisson, and other distributions.

Instructions

Probability distribution operations: PDF, CDF, quantile, mean, variance, sampling

Input Schema

TableJSON Schema

Name	Required	Description	Default
`n`	No	Number of samples (for sample operation)
`x`	No	Point for pdf/cdf/quantile evaluation
`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
`operation`	Yes	One of: pdf, cdf, quantile, mean, variance, sample
`parameters`	Yes	Distribution parameters (e.g. [0, 1] for standard normal)
`distribution`	Yes	Distribution name: normal, exponential, poisson, chi_squared, student_t, uniform, beta, gamma

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

C2.9/5.0

Behavior2/5

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

Annotations declare readOnlyHint=false, idempotentHint=true, and destructiveHint=false, but the description adds no behavioral context: it never mentions that sampling is stochastic, that operations run inside a session workspace (the session param implies state), or what authorization/credential concerns apply. For a tool that writes into a workspace and supports random sampling, this is a significant gap.

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 front-loaded line with no wasted words; the operation list is efficient. However, its extreme brevity means it trades away useful detail rather than being optimally structured for a six-parameter tool.

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 parameter docs are rich. But for a stateful, multi-operation tool with a session/workspace parameter and sampling behavior, the description omits how sessions persist and which operations require which parameters, leaving it only minimally adequate.

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 baseline is 3. The description merely restates the operation names already enumerated in the operation param schema and adds no extra detail about x, n, or parameters beyond what the schema documents.

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?

The description names a specific resource (probability distributions) and enumerates the concrete operations supported (PDF, CDF, quantile, mean, variance, sampling), which maps directly to the required 'operation' parameter. It is clear what the tool does, though it does not distinguish itself from siblings like statistics_summary or evaluate_sage.

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 guidance on when to choose this tool over alternatives such as statistics_summary or evaluate_sage, nor any mention of prerequisites (e.g., that a session/workspace must exist). Usage is only implied by the operation list, leaving the agent to infer routing.

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