Symbolic Algebra MCP Server

create_coordinate_system

Creates a 3D coordinate system for vector calculus operations, optionally with custom coordinate names.

Instructions

Creates a 3D coordinate system for vector calculus operations.

Args:
    name: The name for the coordinate system.
    coord_names: Optional list of coordinate names (3 names for x, y, z).
                If not provided, defaults to [name+'_x', name+'_y', name+'_z'].

Example:
    # Create a coordinate system
    coord_sys = create_coordinate_system("R")
    # Creates a coordinate system R with coordinates R_x, R_y, R_z

    # Create a coordinate system with custom coordinate names
    coord_sys = create_coordinate_system("C", ["rho", "phi", "z"])

Returns:
    The name of the created coordinate system.

Input Schema

Name	Required	Description	Default
`name`	Yes
`coord_names`	No

Output Schema

Name	Required	Description	Default
`result`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

First observedv0.1.0Oct 29, 2026

TDQS

A3.7/5.0

Behavior3/5

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

No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the creation action and the return value (the name), and documents the default coordinate naming behavior. However, it does not disclose whether the coordinate system is persisted in global state, what happens if the name already exists, or any other side effects or error conditions.

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 front-loaded with the core purpose, then structured with Args, Example, and Returns sections. It is appropriately sized for a creation tool with two parameters. Minor redundancy exists because the output schema already covers the return value, but the overall structure is clear and useful.

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 the description need not explain return values, yet it does so redundantly. For a mutation tool with no annotations, the description should ideally mention side effects, persistence, or error behavior. It covers parameters well but leaves behavioral gaps.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters5/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 0%, but the description fully compensates by documenting both parameters: 'name' and 'coord_names', including the default behavior for coord_names ([name+'_x', name+'_y', name+'_z']) and the expected list length (3 names). The examples further clarify usage with concrete values.

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?

The description clearly states a specific verb and resource: 'Creates a 3D coordinate system for vector calculus operations.' This distinguishes it from most siblings, but it does not explicitly differentiate it from related creation tools like create_custom_metric or create_vector_field.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines3/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

The phrase 'for vector calculus operations' implies when the tool is useful, but there are no explicit guidelines about when to prefer this tool over alternatives, nor any exclusions or prerequisites. The examples help clarify invocation but not tool selection.

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