SageMath MCP Server

Polynomial Ring Operation

polynomial_ring_operation

Idempotent

Compute Gröbner bases, ideal dimensions, varieties, and reductions in polynomial rings. Construct rings with specified variables and base fields.

Instructions

Polynomial ring operations: construct rings and compute Groebner bases, ideals, quotients

Input Schema

TableJSON Schema

Name	Required	Description	Default
`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
`base_ring`	No	Base ring	QQ
`operation`	Yes	One of: groebner_basis, ideal_dimension, ideal_variety, reduce, is_groebner
`ring_vars`	Yes	Variable names, e.g. ['a', 'b', 'c']
`polynomials`	Yes	Polynomials as strings, e.g. ['a^2+b', 'b^2-1']

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

C2.6/5.0

Behavior2/5

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

Annotations already provide idempotent/destructive hints, and the description adds little beyond that. It does not disclose whether constructing rings mutates a session workspace, whether some operations are expensive, or how failures might manifest. There is no contradiction with the annotations, but the description does not meaningfully go beyond them.

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?

The description is a single short sentence that is front-loaded and contains no filler words. It is concise, though the brevity contributes to the lack of substantive guidance.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness2/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

For a tool with five parameters, five distinct operations, and a session/workspace concept, this description is too thin for an agent to select and invoke it confidently. The output schema may document results, but operation semantics and workspace-state implications remain underspecified.

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 repeats some nouns like rings and Groebner bases but adds no extra meaning about how base_ring, polynomials, operation, or session interact. It does not compensate beyond what the schema already provides.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose3/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description identifies the domain ('polynomial ring operations') and mentions constructing rings and computing Groebner bases, ideals, and quotients, so the resource is clear. However, it is a category-level phrase rather than a specific verb+resource statement, and it omits several actual operations such as reduce, is_groebner, ideal_dimension, and ideal_variety. It also does not explicitly distinguish itself from the many other math *_operation sibling tools.

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 about when to use this tool instead of siblings like solve_equation, factor_expression, or group_operation. The phrase 'polynomial ring operations' implies a domain, but no exclusions, prerequisites, or alternative tool mentions are provided.

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