SageMath MCP Server

symbolic_sum

Idempotent

Computes closed-form symbolic sums and products over an index variable, including infinite series. Use it to evaluate summations like 1/n^2 exactly instead of numeric approximation.

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 declare idempotentHint=true, destructiveHint=false, and openWorldHint=false, so the safety profile is largely carried by structured data. The description adds only the 'including infinite series' scope note; it does not explain anything about evaluation limits, timeouts, or the odd readOnlyHint=false flag on a pure computation. Adds some value but not rich context.

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 sibling-routing advice. 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?

An output schema exists, so return values need not be explained, and all six parameters are covered by the schema. The description supplies purpose and sibling routing, which is sufficient to call it correctly; only minor behavioral depth (e.g. infinite-series convergence handling) is 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 every parameter (lower, upper, product, session, variable, expression) is already documented in the schema, including defaults and the session bearer-credential warning. The description adds no syntax or format detail beyond that, 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?

States a specific verb and resource ('Closed form of a symbolic sum or product over an index variable'), and explicitly names the sibling it should be chosen over (evaluate_sage). An agent can distinguish it from evaluate_sage without opening either 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?

Gives a clear selection rule: 'Prefer this over evaluate_sage for summations.' This names the alternative and the condition that selects it. It stops short of a full 5 because it states no when-not/exclusion cases (e.g. numeric-only evaluation or cases where evaluate_sage is still correct).

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