Symbolic Algebra MCP Server

calculate_curl

Computes the curl of a symbolic vector field and returns a key for the resulting expression.

Instructions

Calculates the curl of a vector field using SymPy's curl function.

Args:
    vector_field_key: The key of the vector field expression.

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

    # Create a vector field F = (y, -x, 0)
    vector_field = create_vector_field("R", "R_y", "-R_x", "0")

    # Calculate curl
    curl_result = calculate_curl(vector_field)
    # Returns (0, 0, -2)

Returns:
    A key for the curl expression.

Input Schema

Name	Required	Description	Default
`vector_field_key`	Yes

Output Schema

Name	Required	Description	Default
`result`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

First observedv0.1.0Oct 29, 2026

TDQS

A3.8/5.0

Behavior3/5

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

No annotations are provided, so the description carries the burden. It does disclose that the result is a key rather than an expanded expression, but there is a mild inconsistency: the prose says 'Returns: A key for the curl expression' while the example comment says '# Returns (0, 0, -2)'. It says nothing about error conditions, dimensional requirements, or whether the expression is auto-simplified.

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?

Purpose is front-loaded in a single sentence, followed by Args/Example/Returns sections. The example is multi-line but earns its place by demonstrating the required call sequence rather than merely restating parameters.

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 detail is covered elsewhere, and the description still names the return type. For a one-parameter tool with a clear prerequisite workflow, the main remaining gap is unstated failure modes (e.g., non-3D fields).

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 coverage is 0% – the schema only names 'vector_field_key' as a string. The description compensates by defining it as 'the key of the vector field expression' and the example shows it is the value returned by create_vector_field, so the agent knows where to obtain it.

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?

States a specific verb and resource: 'Calculates the curl of a vector field using SymPy's curl function.' An agent can distinguish this from calculate_divergence and calculate_gradient by name, though the description never explicitly contrasts them.

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?

The worked example makes the prerequisite chain explicit: create_coordinate_system first, then create_vector_field, then calculate_curl. That is real usage guidance for a stateful CAS tool, though there are no stated exclusions or conditions where curl is inapplicable.

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