learn-physics-0.6.2: Haskell code for learning physics

Copyright(c) Scott N. Walck 2011-2018
LicenseBSD3 (see LICENSE)
MaintainerScott N. Walck <walck@lvc.edu>
Stabilityexperimental
Safe HaskellSafe
LanguageHaskell98

Physics.Learn.CarrotVec

Contents

Description

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.

Synopsis

Documentation

data Vec Source #

A type for vectors.

Instances

Eq Vec Source # 

Methods

(==) :: Vec -> Vec -> Bool #

(/=) :: Vec -> Vec -> Bool #

Show Vec Source # 

Methods

showsPrec :: Int -> Vec -> ShowS #

show :: Vec -> String #

showList :: [Vec] -> ShowS #

StateSpace Vec Source # 

Associated Types

type Diff Vec :: * Source #

Methods

(.-.) :: Vec -> Vec -> Diff Vec Source #

(.+^) :: Vec -> Diff Vec -> Vec Source #

type Scalar Vec # 
type Diff Vec Source # 
type Diff Vec = Vec

xComp :: Vec -> Double Source #

x component

yComp :: Vec -> Double Source #

y component

zComp :: Vec -> Double Source #

z component

vec Source #

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 infixl 6 #

Add vectors

(^-^) :: AdditiveGroup v => v -> v -> v infixl 6 #

Group subtraction

(*^) :: VectorSpace v => Scalar v -> v -> v infixr 7 #

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 infixr 7 #

Inner/dot product

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

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 Source #

Unit vector in the x direction.

jHat :: Vec Source #

Unit vector in the y direction.

kHat :: Vec Source #

Unit vector in the z direction.

Orphan instances

VectorSpace Vec Source # 

Associated Types

type Scalar Vec :: * #

Methods

(*^) :: Scalar Vec -> Vec -> Vec #

InnerSpace Vec Source # 

Methods

(<.>) :: Vec -> Vec -> Scalar Vec #

AdditiveGroup Vec Source # 

Methods

zeroV :: Vec #

(^+^) :: Vec -> Vec -> Vec #

negateV :: Vec -> Vec #

(^-^) :: Vec -> Vec -> Vec #