Physics.Learn.CarrotVec

This module defines some basic vector functionality. It uses the same internal data representation as SimpleVec, but declares Vec to be an instance of VectorSpace. We import zeroV, negateV, sumV, ^+^, ^-^ from AdditiveGroup, and *^, ^*, ^/, <.>, magnitude from VectorSpace.

CarrotVec exports exactly the same symbols as SimpleVec; they are just defined differently.

Documentation

data Vec

A type for vectors.

Instances

Eq Vec

Show Vec

StateSpace Vec

type Scalar Vec = Double

type Diff Vec = Vec

xComp :: Vec -> Double

x component

yComp :: Vec -> Double

y component

zComp :: Vec -> Double

z component

vec

Arguments

:: Double

x component

-> Double

y component

-> Double

z component

-> Vec

Form a vector by giving its x, y, and z components.

(^+^) :: AdditiveGroup v => v -> v -> v

Add vectors

(^-^) :: AdditiveGroup v => v -> v -> v

Group subtraction

(*^) :: VectorSpace v => Scalar v -> v -> v

Scale a vector

(^*) :: (VectorSpace v, (~) * s (Scalar v)) => v -> s -> v infixl 7

Vector multiplied by scalar

(^/) :: (VectorSpace v, (~) * s (Scalar v), Fractional s) => v -> s -> v infixr 7

Vector divided by scalar

(<.>) :: InnerSpace v => v -> v -> Scalar v

Inner/dot product

(><) :: Vec -> Vec -> Vec infixl 7

Cross product.

magnitude :: (InnerSpace v, (~) * s (Scalar v), Floating s) => v -> s

Length of a vector. See also magnitudeSq.

zeroV :: AdditiveGroup v => v

The zero element: identity for '(^+^)'

negateV :: AdditiveGroup v => v -> v

Additive inverse

sumV :: (Foldable f, AdditiveGroup v) => f v -> v

Sum over several vectors

iHat :: Vec

Unit vector in the x direction.

jHat :: Vec

Unit vector in the y direction.

kHat :: Vec

Unit vector in the z direction.