Vector

The vector module provides tools for basic vector math and differential calculus with respect to 3D Cartesian coordinate systems. This documentation provides an overview of all the features offered, and relevant API.

Guide to Vector

• Introduction
  • Vectors and Scalars
  • Coordinate Systems
  • Fields
• Basic Implementation details
  • Coordinate Systems and Vectors
  • SymPy operations on Vectors
  • Points
  • Dyadics
• More about Coordinate Systems
  • Locating new systems
  • Orienting new systems
  • Orienting AND Locating new systems
  • Transforming new system
  • Expression of quantities in different coordinate systems
• Scalar and Vector Field Functionality
  • Implementation in sympy.vector
  • Field operators and related functions
  • Field operator in orthogonal curvilinear coordinate system
  • Conservative and Solenoidal fields
  • Scalar potential functions
• General examples of usage
  • Quadrilateral problem
  • Third product rule for Del operator
• Applications of Vector Integrals
  • Calculation of Perimeter, Surface Area, and Volume
  • Calculation of mass of a body
  • Calculation of Flux
  • Verifying Stoke’s Theorem
  • Verifying Divergence Theorem

Vector API

• Essential Classes in sympy.vector (docstrings)
  • CoordSys3D
  • Vector
  • Dyadic
  • Del
  • ParametricRegion
  • ImplicitRegion
  • ParametricIntegral
• Orienter classes (docstrings)
  • Orienter
  • AxisOrienter
  • BodyOrienter
  • SpaceOrienter
  • QuaternionOrienter
• Essential Functions in sympy.vector (docstrings)
  • matrix_to_vector
  • express
  • curl
  • divergence
  • gradient
  • is_conservative
  • is_solenoidal
  • scalar_potential
  • scalar_potential_difference
  • vector_integrate

References for Vector

Dyadics

https://en.wikipedia.org/wiki/Dyadics

DyadicProducts

https://en.wikipedia.org/wiki/Dyadic_product

DelOperator

https://en.wikipedia.org/wiki/Del