SageMath MCP Server

factor_expression

Idempotent

Factor mathematical expressions or integers into prime factors or simpler terms, helping simplify polynomials and solve equations.

Instructions

Factor a mathematical expression or integer

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
`expression`	Yes	Expression to factor (e.g., 'x^2 - 1' or '60')

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 already provide the safety profile (readOnlyHint=false, idempotentHint=true, destructiveHint=false), and the description adds nothing beyond them. It does not explain that the tool operates within a session/workspace, whether results are stored, or how the odd readOnlyHint=false with idempotentHint=true combination manifests.

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 sentence with zero padding. It is efficient, though arguably too thin given the complexity of the sibling landscape it must be distinguished from.

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 parameters are fully covered by the schema. The remaining gap is routing guidance against the many overlapping symbolic siblings, which the description does not address.

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 both parameters are documented in the schema, and the description only echoes the expression parameter. The session/workspace semantics are fully handled by the schema, so the baseline 3 is appropriate.

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?

States a specific verb and resource ('Factor a mathematical expression or integer'), and the 'or integer' clause usefully signals it handles numeric input as well as symbolic input. However, it does not distinguish itself from close siblings like simplify_expression or expand_expression, leaving the agent to infer the difference.

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 when-to-use guidance and no mention of alternatives, despite a large sibling set (simplify_expression, expand_expression, calculate_expression, solve_equation) that plausibly overlaps. The agent gets no signal about when factoring is the right operation versus those.

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