brainrake / elm-ganja / Ganja.Pga3d

Clifford Algebra: Pga3d

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Basis


type Pga3dBasis
    = Scalar
    | E0
    | E1
    | E2
    | E3
    | E01
    | E02
    | E03
    | E12
    | E31
    | E23
    | E021
    | E013
    | E032
    | E123
    | E0123

Basis type

basisList : List Pga3dBasis

Basis list

basisCount : Basics.Int

Number of coefficients

basisName : Pga3dBasis -> String

Basis name

Multivector


type Pga3d
    = Pga3d 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 : Pga3d

Zero value

get : Pga3dBasis -> Pga3d -> Basics.Float

Get coefficient

set : Pga3dBasis -> Basics.Float -> Pga3d -> Pga3d

Update coefficient

new : Basics.Float -> Pga3dBasis -> Pga3d

Multivector with one coefficient

Basis multivectors

unitScalar : Pga3d

Basis multivector

e0 : Pga3d

Basis multivector

e1 : Pga3d

Basis multivector

e2 : Pga3d

Basis multivector

e3 : Pga3d

Basis multivector

e01 : Pga3d

Basis multivector

e02 : Pga3d

Basis multivector

e03 : Pga3d

Basis multivector

e12 : Pga3d

Basis multivector

e31 : Pga3d

Basis multivector

e23 : Pga3d

Basis multivector

e021 : Pga3d

Basis multivector

e013 : Pga3d

Basis multivector

e032 : Pga3d

Basis multivector

e123 : Pga3d

Basis multivector

e0123 : Pga3d

Basis multivector

Conversion

toString : Pga3d -> String

Convert multivector to string

fromList : List Basics.Float -> Maybe Pga3d

Convert list of coefficients to multivector

toList : Pga3d -> List Basics.Float

Convert multivector to list of coefficients

Unary Operators

reverse : Pga3d -> Pga3d

Reverse the order of the basis blades.

dual : Pga3d -> Pga3d

Poincare duality operator.

conjugate : Pga3d -> Pga3d

Clifford Conjugation

involute : Pga3d -> Pga3d

Main involution

Binary Operators

mul : Pga3d -> Pga3d -> Pga3d

The geometric product.

wedge : Pga3d -> Pga3d -> Pga3d

The outer product. (MEET)

vee : Pga3d -> Pga3d -> Pga3d

The regressive product. (JOIN)

dot : Pga3d -> Pga3d -> Pga3d

The inner product.

add : Pga3d -> Pga3d -> Pga3d

Multivector addition

sub : Pga3d -> Pga3d -> Pga3d

Multivector subtraction

smul : Basics.Float -> Pga3d -> Pga3d

scalar/multivector multiplication

muls : Pga3d -> Basics.Float -> Pga3d

multivector/scalar multiplication

sadd : Basics.Float -> Pga3d -> Pga3d

scalar/multivector addition

adds : Pga3d -> Basics.Float -> Pga3d

multivector/scalar addition

ssub : Basics.Float -> Pga3d -> Pga3d

scalar/multivector subtraction

subs : Pga3d -> Basics.Float -> Pga3d

multivector/scalar subtraction

Norm

norm : Pga3d -> Basics.Float

Norm

inorm : Pga3d -> Basics.Float

Norm of dual

normalized : Pga3d -> Pga3d

Normalized multivector