hTensor-0.1.0: Multidimensional arrays and simple tensor computations.Source codeContentsIndex
Numeric.LinearAlgebra.Exterior
Stabilityexperimental
MaintainerAlberto Ruiz <aruiz@um.es>
Description
Exterior Algebra.
Synopsis
(/\) :: Coord t => Tensor t -> Tensor t -> Tensor t
inner :: Coord t => Tensor t -> Tensor t -> Tensor t
leviCivita :: Int -> Tensor Double
dual :: Tensor Double -> Tensor Double
(\/) :: Tensor Double -> Tensor Double -> Tensor Double
module Numeric.LinearAlgebra.Tensor
asMultivector :: Tensor Double -> Multivector
fromMultivector :: Int -> Multivector -> Tensor Double
Documentation
(/\) :: Coord t => Tensor t -> Tensor t -> Tensor tSource

The exterior (wedge) product of two tensors. Obtains the union of subspaces.

Implemented as the antisymmetrization of the tensor product.

inner :: Coord t => Tensor t -> Tensor t -> Tensor tSource
Euclidean inner product of multivectors.
leviCivita :: Int -> Tensor DoubleSource
The full antisymmetric tensor of rank n (contravariant version).
dual :: Tensor Double -> Tensor DoubleSource

Inner product of a r-vector with the whole space.

dual t = inner (leviCivita n) t
(\/) :: Tensor Double -> Tensor Double -> Tensor DoubleSource

The "meet" operator. Obtains the intersection of subspaces.

a \/ b = dual (dual a /\ dual b)
module Numeric.LinearAlgebra.Tensor
asMultivector :: Tensor Double -> MultivectorSource

Extract a compact multivector representation from a full antisymmetric tensor.

asMultivector = Multivector.fromTensor.

(We do not check that the tensor is actually antisymmetric.)

fromMultivector :: Int -> Multivector -> Tensor DoubleSource
Create an explicit antisymmetric Tensor from the components of a Multivector of a given grade.
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