| Copyright | (c) Alberto Ruiz 2009 |
|---|---|
| License | BSD3 |
| Maintainer | Alberto Ruiz |
| Stability | experimental |
| Safe Haskell | None |
| Language | Haskell98 |
Numeric.LinearAlgebra.Multivector
Description
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
data Multivector Source #
Instances
scalar :: Double -> Multivector Source #
Creates a scalar multivector.
vector :: [Double] -> Multivector Source #
Creates a grade 1 multivector of from a list of coordinates.
e :: Int -> Multivector Source #
The k-th basis element.
(/\) :: Multivector -> Multivector -> Multivector infixl 7 Source #
The exterior (outer) product.
(-|) :: Multivector -> Multivector -> Multivector infixl 7 Source #
The contractive inner product.
(\/) :: Multivector -> Multivector -> Multivector infixl 7 Source #
Intersection of subspaces.
rever :: Multivector -> Multivector Source #
The reversion operator.
full :: Int -> Multivector Source #
The full space of the given dimension. This is the leviCivita simbol, and the basis of the pseudoscalar.
Arguments
| :: Int | dimension of the space |
| -> Double | angle |
| -> Multivector | axis |
| -> Multivector | result |
The rotor operator, used in a sandwich product.
apply :: (Int -> Multivector) -> Multivector -> Multivector Source #
Apply a linear transformation, expressed as the image of the element i-th of the basis.
(This is a monadic bind!)
grade :: Int -> Multivector -> Multivector Source #
maxGrade :: Multivector -> Int Source #
maxDim :: Multivector -> Int Source #
fromTensor :: Tensor Double -> Multivector Source #
Extract a multivector representation from a full antisymmetric tensor.
(We do not check that the tensor is actually antisymmetric.)