SageMath MCP Server

matrix_multiply

Idempotent

Multiply two matrices and return nested lists. Supports exact integer arithmetic, including values above 2^53 passed as decimal strings.

Instructions

Multiply two matrices and return the result as nested lists

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
`matrix_a`	Yes	Left matrix (rows of numbers). Integers stay exact; pass values from 2^53 up as decimal strings, e.g. "9007199254740993".
`matrix_b`	Yes	Right matrix (rows of numbers). Integers stay exact.

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'."

Changed7 schema fields changedv0.5.0Aug 14, 2026

changedInput schema / properties / matrix_a / description

Previous value: -"Left matrix (rows of numbers)"New value: +"Left matrix (rows of numbers). Integers stay exact; pass values from 2^53 up as decimal strings, e.g. \"9007199254740993\"."

addedInput schema / properties / matrix_a / items / items / anyOf

Added value: +[
+  {
+    "type": "number"
+  },
+  {
+    "type": "integer"
+  },
+  {
+    "type": "string"
+  }
+]

removedInput schema / properties / matrix_a / items / items / type
```
Removed value: -"number"
```

changedInput schema / properties / matrix_b / description

Previous value: -"Right matrix (rows of numbers)"New value: +"Right matrix (rows of numbers). Integers stay exact."

addedInput schema / properties / matrix_b / items / items / anyOf

Added value: +[
+  {
+    "type": "number"
+  },
+  {
+    "type": "integer"
+  },
+  {
+    "type": "string"
+  }
+]

removedInput schema / properties / matrix_b / items / items / type
```
Removed value: -"number"
```

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 and idempotentHint=true, implying stateful/workspace behavior, but the description says nothing about the session workspace, whether results are stored, or how the computation interacts with workspace variables. It only restates the return format, which the output schema already covers.

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 tight sentence with no wasted words and the core action front-loaded. It is just sparse rather than bloated, so no penalty for verbosity.

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?

The tool takes a session/workspace parameter whose semantics (independent variables, cross-reconnect handles) are non-trivial, yet the description omits it entirely and gives no routing versus 'matrix_operation'. Low operation complexity and an existing output schema mitigate this, but key context is missing.

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 matrix_a, matrix_b (including the 2^53 string convention) and the session parameter in detail. The description adds no extra parameter meaning, 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?

Clear specific verb + resource (multiply two matrices) and it states the return shape. However it does nothing to distinguish itself from the sibling 'matrix_operation', which an agent would reasonably consider for the same task.

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 or when-not-to-use guidance, and no mention of the closely related 'matrix_operation' sibling that could also perform matrix math. The agent must guess which one applies.

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