calculate_gradient

Compute the gradient vector field of a given scalar field using symbolic algebra. Ideal for calculating directional derivatives and analyzing scalar fields in mathematical and scientific applications.

Instructions

Calculates the gradient of a scalar field using SymPy's gradient function.

Args:
    scalar_field_key: The key of the scalar field expression.

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

    # Create a scalar field f = x^2 + y^2 + z^2
    scalar_field = introduce_expression("R_x**2 + R_y**2 + R_z**2")

    # Calculate gradient
    grad_result = calculate_gradient(scalar_field)
    # Returns (2x, 2y, 2z)

Returns:
    A key for the gradient vector field expression.

Input Schema

Name	Required	Description	Default
`scalar_field_key`	Yes

Input Schema (JSON Schema)

{
  "properties": {
    "scalar_field_key": {
      "title": "Scalar Field Key",
      "type": "string"
    }
  },
  "required": [
    "scalar_field_key"
  ],
  "title": "calculate_gradientArguments",
  "type": "object"
}

Symbolic Algebra MCP Server

calculate_gradient

Instructions

Input Schema

Input Schema (JSON Schema)

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