Symbolic Algebra MCP Server

create_vector_field

Builds a vector field in a chosen coordinate system from x, y, and z component expressions, enabling symbolic vector calculus and field analysis.

Instructions

Creates a vector field in the specified coordinate system.

Args:
    coord_sys_name: The name of the coordinate system to use.
    component_x: String expression for the x-component of the vector field.
    component_y: String expression for the y-component of the vector field.
    component_z: String expression for the z-component of the vector field.

Example:
    # First create a coordinate system
    create_coordinate_system("R")

    # Create a vector field F = (y, -x, z)
    vector_field = create_vector_field("R", "R_y", "-R_x", "R_z")

Returns:
    A key for the vector field expression.

Input Schema

Name	Required	Description	Default
`component_x`	Yes
`component_y`	Yes
`component_z`	Yes
`coord_sys_name`	Yes

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 behavioral burden. It discloses that the tool creates a vector field and returns a key, and the example shows prerequisite ordering, but it does not describe side effects, persistence, error behavior, or permissions.

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?

The description is front-loaded with the core purpose and then structured into Args, Example, and Returns. Given the zero schema description coverage, the parameter documentation and example each earn their place without unnecessary verbosity.

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-value explanation is not strictly required, but the description still states that a key is returned. Parameter meanings and a prerequisite example are included, making the definition complete enough for correct invocation, though it could say more about how the returned key is used downstream.

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

Parameters4/5

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

Schema description coverage is 0%, but the description compensates by explaining each parameter's meaning: coord_sys_name names the coordinate system, and component_x/y/z are string expressions for the vector components. The example further clarifies expression syntax, though constraints on valid expressions are not detailed.

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 states a specific verb and resource: it creates a vector field in a specified coordinate system. The purpose is clear, but it does not explicitly differentiate itself from sibling creation tools such as create_coordinate_system or create_custom_metric.

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 example implies a prerequisite by showing create_coordinate_system first, which is useful context. However, it does not state when to use this tool versus alternatives or describe any exclusions.

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