FriCAS :: DifferentialForms

Contents:

• 1 Theory
  • 1.0 Introduction
  • 1.1 Definitions
    • 1.1.1 Inner product of differential forms (dot)
    • 1.1.2. The volume form \(\eta\) (volumeForm)
    • 1.1.3. Hodge dual (hodgeStar)
    • 1.1.4 Interior product (interiorProduct)
    • 1.1.5 The Lie derivative (lieDerivative)
    • 1.1.6 The CoDifferential \(\delta\) (codifferential)
    • 1.1.7 The sign of a metric \(s(g)\) (s)
    • 1.1.8 The inverse Hodge star \(\star^{-1}\) (invHodgeStar)
    • 1.1.9 The Hodge-Laplacian \(\Delta_g\) (hodgeLaplacian)
  • Bibliography
• 2 Export
  • 2.0 Package Details
  • 2.1 The metric g
  • 2.2 Exported Functions
    • 2.2.1 Volume Form
    • 2.2.1 Scalar Product
    • 2.2.2 Hodge Star Operator
    • 2.2.3 Interior Product
    • 2.2.4 Lie Derivative
    • 2.2.5 Projection
    • 2.2.6 Monomials
    • 2.2.7 Atomize Basis Term
    • 2.2.8 Conjugate Basis Term
    • 2.2.9 Scalar and Vector Field
    • 2.2.10 Miscellaneous Functions
• 3 Implementation
  • 3.0 Implementation Notes
    • 3.1 Internal Representation
    • 3.2 dot :: inner product
    • 3.3 hodgeStar :: Hodge dual
    • 3.4 interiorProduct :: Interior product
    • 3.5 lieDerivative :: Lie derivative
    • 3.6 proj :: Projection
• 4 Usage
  • 4.0 Examples
    • 4.1 Calculus in \(\mathbb{R}^3\)
    • 4.2 Faraday 2-form
    • 4.3 Some Examples from Maple
    • 4.4 More examples (way of working)

Indices and tables

• Index
• Module Index
• Search Page