Stability | experimental |
---|---|
Maintainer | Alberto Ruiz <aruiz@um.es> |
Safe Haskell | Safe-Infered |
A simple implementation of Geometric Algebra.
The Num instance provides the geometric product, and the Fractional instance provides the inverse of multivectors.
This module provides a simple Euclidean embedding.
- data Multivector
- coords :: Multivector -> [(Double, [Int])]
- scalar :: Double -> Multivector
- vector :: [Double] -> Multivector
- e :: Int -> Multivector
- (/\) :: Multivector -> Multivector -> Multivector
- (-|) :: Multivector -> Multivector -> Multivector
- (\/) :: Multivector -> Multivector -> Multivector
- rever :: Multivector -> Multivector
- full :: Int -> Multivector
- rotor :: Int -> Double -> Multivector -> Multivector
- apply :: (Int -> Multivector) -> Multivector -> Multivector
- grade :: Int -> Multivector -> Multivector
- maxGrade :: Multivector -> Int
- maxDim :: Multivector -> Int
- fromTensor :: Tensor Double -> Multivector
Documentation
coords :: Multivector -> [(Double, [Int])]Source
scalar :: Double -> MultivectorSource
Creates a scalar multivector.
vector :: [Double] -> MultivectorSource
Creates a grade 1 multivector of from a list of coordinates.
e :: Int -> MultivectorSource
The k-th basis element.
(/\) :: Multivector -> Multivector -> MultivectorSource
The exterior (outer) product.
(-|) :: Multivector -> Multivector -> MultivectorSource
The contractive inner product.
(\/) :: Multivector -> Multivector -> MultivectorSource
Intersection of subspaces.
rever :: Multivector -> MultivectorSource
The reversion operator.
full :: Int -> MultivectorSource
The full space of the given dimension. This is the leviCivita simbol, and the basis of the pseudoscalar.
:: Int | dimension of the space |
-> Double | angle |
-> Multivector | axis |
-> Multivector | result |
The rotor operator, used in a sandwich product.
apply :: (Int -> Multivector) -> Multivector -> MultivectorSource
Apply a linear transformation, expressed as the image of the element i-th of the basis.
(This is a monadic bind!)
grade :: Int -> Multivector -> MultivectorSource
maxGrade :: Multivector -> IntSource
maxDim :: Multivector -> IntSource
fromTensor :: Tensor Double -> MultivectorSource
Extract a multivector representation from a full antisymmetric tensor.
(We do not check that the tensor is actually antisymmetric.)