brainrake / elm-ganja / Ganja.Spacetime

Clifford Algebra: Spacetime

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Basis


type SpacetimeBasis
    = Scalar
    | E1
    | E2
    | E3
    | E4
    | E12
    | E13
    | E14
    | E23
    | E24
    | E34
    | E123
    | E124
    | E134
    | E234
    | E1234

Basis type

basisList : List SpacetimeBasis

Basis list

basisCount : Basics.Int

Number of coefficients

basisName : SpacetimeBasis -> String

Basis name

Multivector


type Spacetime
    = Spacetime Basics.Float Basics.Float Basics.Float Basics.Float Basics.Float Basics.Float Basics.Float Basics.Float Basics.Float Basics.Float Basics.Float Basics.Float Basics.Float Basics.Float Basics.Float Basics.Float

Multivector

zero : Spacetime

Zero value

get : SpacetimeBasis -> Spacetime -> Basics.Float

Get coefficient

set : SpacetimeBasis -> Basics.Float -> Spacetime -> Spacetime

Update coefficient

new : Basics.Float -> SpacetimeBasis -> Spacetime

Multivector with one coefficient

Basis multivectors

unitScalar : Spacetime

Basis multivector

e1 : Spacetime

Basis multivector

e2 : Spacetime

Basis multivector

e3 : Spacetime

Basis multivector

e4 : Spacetime

Basis multivector

e12 : Spacetime

Basis multivector

e13 : Spacetime

Basis multivector

e14 : Spacetime

Basis multivector

e23 : Spacetime

Basis multivector

e24 : Spacetime

Basis multivector

e34 : Spacetime

Basis multivector

e123 : Spacetime

Basis multivector

e124 : Spacetime

Basis multivector

e134 : Spacetime

Basis multivector

e234 : Spacetime

Basis multivector

e1234 : Spacetime

Basis multivector

Conversion

toString : Spacetime -> String

Convert multivector to string

fromList : List Basics.Float -> Maybe Spacetime

Convert list of coefficients to multivector

toList : Spacetime -> List Basics.Float

Convert multivector to list of coefficients

Unary Operators

reverse : Spacetime -> Spacetime

Reverse the order of the basis blades.

dual : Spacetime -> Spacetime

Poincare duality operator.

conjugate : Spacetime -> Spacetime

Clifford Conjugation

involute : Spacetime -> Spacetime

Main involution

Binary Operators

mul : Spacetime -> Spacetime -> Spacetime

The geometric product.

wedge : Spacetime -> Spacetime -> Spacetime

The outer product. (MEET)

vee : Spacetime -> Spacetime -> Spacetime

The regressive product. (JOIN)

dot : Spacetime -> Spacetime -> Spacetime

The inner product.

add : Spacetime -> Spacetime -> Spacetime

Multivector addition

sub : Spacetime -> Spacetime -> Spacetime

Multivector subtraction

smul : Basics.Float -> Spacetime -> Spacetime

scalar/multivector multiplication

muls : Spacetime -> Basics.Float -> Spacetime

multivector/scalar multiplication

sadd : Basics.Float -> Spacetime -> Spacetime

scalar/multivector addition

adds : Spacetime -> Basics.Float -> Spacetime

multivector/scalar addition

ssub : Basics.Float -> Spacetime -> Spacetime

scalar/multivector subtraction

subs : Spacetime -> Basics.Float -> Spacetime

multivector/scalar subtraction

Norm

norm : Spacetime -> Basics.Float

Norm

inorm : Spacetime -> Basics.Float

Norm of dual

normalized : Spacetime -> Spacetime

Normalized multivector