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DifferentialGeometry

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DifferentialGeometry/DGNullSpace
find the null space of a linear transformation acting on a vector space of vectors, differential forms, tensors

DifferentialGeometry/DGsolve
solve a list of tensor equations for an unknown list of tensors

DifferentialGeometry/DGconjugate
find the complex conjugate of a vector, tensor or differential form; find the conjugate of a quaternion or octonion

DifferentialGeometry/AlgebraicOperations
addition, subtraction, scalar multiplication, wedge product, tensor product

DifferentialGeometry/Annihilator
find the subspace of vectors (or 1-forms) whose interior product with a given list of 1-forms (or vectors) vanishes

DifferentialGeometry/ApplyTransformation
evaluate a transformation at a point

DifferentialGeometry/ChangeFrame
change the current or active frame

DifferentialGeometry/ComplementaryBasis
extend a basis for a subspace to a basis for a larger subspace

DifferentialGeometry/ComposeTransformations
compose a sequence of two or more transformations

DifferentialGeometry/Convert
convert routines of the DifferentialGeometry package

DifferentialGeometry/DGbasis
calculate the dual basis to a given basis of vectors or 1-forms

DifferentialGeometry/DGsetup
set up a coordinate system, a frame, a Lie algebra, define a set of abstract forms

DifferentialGeometry/DGzip
form a linear combination, wedge product or tensor product of a list of vectors, forms or tensors

DifferentialGeometry/DeRhamHomotopy
apply the homotopy operator for the de Rham complex on R^n to a differential form

DifferentialGeometry/DualBasis
calculate the dual basis to a given basis of vectors or 1-forms

DifferentialGeometry/ExteriorDerivative
take the exterior derivative of a differential form

DifferentialGeometry/Flow
calculate the one parameter group of differeomorphisms (flow) of a vector field

DifferentialGeometry/FrameData
calculate the structure equations for a generic (anholonomic) frame

DifferentialGeometry/GetComponents
find the coefficients of a vector, differential form or tensor with respect to a list of vectors, differential forms or tensors

DifferentialGeometry/Hook
form the interior product of a vector or a list of vectors with a differential form

DifferentialGeometry/InfinitesimalTransformation
compute the Lie algebra of infinitesimal generators for an action of a Lie group on a manifold

DifferentialGeometry/IntegrateForm
evaluate a p-fold iterated integral of a differential p-form

DifferentialGeometry/IntersectSubspaces
find the intersection of a list of vector subspaces of vectors, forms or tensors

DifferentialGeometry/InverseTransformation
find the inverse of a transformation

DifferentialGeometry/LieBracket
calculate the Lie bracket of two vector fields or 2 vectors in a Lie algebra

DifferentialGeometry/LieDerivative
calculate the Lie derivative of a vector field, differential form, tensor, or connection with respect to a vector field

DifferentialGeometry/Preferences
DifferentialGeometry[Preferences]

DifferentialGeometry/Pullback
pullback a differential p-form by the Jacobian of a transformation

DifferentialGeometry/PullbackVector
find (if possible) a vector field whose pushforward by the Jacobian of a given transformation is a given vector field

DifferentialGeometry/Pushforward
pushforward a vector or a vector field by the Jacobian of a transformation

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