SageMath MCP Server

Symbolic Sum

symbolic_sum

Idempotent

Compute closed-form expressions for symbolic sums and products over an index variable, including infinite series. Enter the expression, bounds, and variable to get an exact result.

Instructions

Closed form of a symbolic sum or product over an index variable, including infinite series. Prefer this over evaluate_sage for summations.

Input Schema

TableJSON Schema

Name	Required	Description	Default
`lower`	No	Lower bound (e.g. '1')	1
`upper`	No	Upper bound (e.g. 'oo' for infinity)	oo
`product`	No	If true, compute a product instead of a sum
`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
`variable`	No	Index variable (e.g. 'n')	n
`expression`	Yes	Expression to sum (e.g. '1/n^2')

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 already convey idempotence and non-destructiveness. The description adds useful behavior about closed-form computation and infinite-series support, which goes beyond annotations. It does not mention failure modes when no closed form exists, but the output schema likely covers return behavior.

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 short sentences, front-loading the main capability and then giving a decisive sibling-routing recommendation. No filler or redundancy; every sentence earns its place.

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?

For a compute tool with a rich schema and output schema, the description covers the key use case and the most important sibling distinction. It is complete enough for an agent to select and invoke it correctly; only minor behavioral details like fallback when no closed form exists are absent.

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 schema already documents all six parameters. The description adds only a high-level note about summations/products and infinite series, which does not materially deepen parameter understanding beyond the schema.

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?

States a specific operation ('closed form of a symbolic sum or product over an index variable') and explicitly distinguishes itself from evaluate_sage for summations. The domain and scope are clear even without opening the schema.

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 says to prefer this tool over evaluate_sage for summations, naming the sibling and the condition. It does not discuss exclusions or alternatives for products, but the core guidance for choose-vs-evaluate_sage is direct and actionable.

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