Quaternion

290a11e2-7a90-45aa-a978-05456bae0808 5 15 12 decimal

&[DATE] &[TIME] - &[FILENAME]

Uniform ...  -1 < rnd < 1 n rnd μ n 11 line : 2 μ Random * 1 - 21 line :

MAT n 5000 : X n rnd : Y n rnd : Z n rnd : 31 line X abs vectorize Y abs vectorize Z abs vectorize augment 31 line :

Quaternions system.
native modulo 6 permute
go to permute oder 'j' α 0.75 : β 0.25 - : 12 mat vectormodulo 2 : (select modulo[1,2] ≡ 21 sys

Quaternion

1. Instruct/code the solver a b GivenFind a b FindRoot :

Solutions from the GivenFind solver are in lexicographic order wrt "init".

init 1 :

2. System to solve v1 p q + r - 0 ≡ p 2^q 2^+ r 2^+ 1 ≡ α p * β r * + 0 ≡ 31 mat :_v2 p init ≡ q init ≡ r init ≡ 31 mat : 13 mat

Observe:

1. init [10e-15] => col(modulo,1)

2. init [1] => col(modulo,2)

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solutions p q r 31 mat ≡

Quaternion v1 v2 GivenFind : 0.267 - 0.535 - 0.802 - 31 mat

p q r 31 mat 0.267 - 0.535 - 0.802 - 31 mat

3. Define the Quaternion "modulo"
... and the Quaternion vector modulo 2 β 2^* 2 β * α * + 2 α 2^* + sqrt :

V β - modulo / β modulo / β α + (modulo / β α + (- modulo / α modulo / α - modulo / 32 mat : 0.2673 0.2673 - 0.5345 0.5345 - 0.8018 0.8018 - 32 mat

4. Create the Quaternion vector ω V vectormodulo col V 11 el stack :

ω 0.2673 - 0.5345 - 0.8018 - 0.2673 41 mat

Euclidean norm => Quaternion vector ω 1 el 2^ω 2 el 2^+ ω 3 el 2^+ ω 4 el 2^+ sqrt 1.035

ω norme 1.035

# norme Euclidean norm ≡

5. Define the "UnitV", apply to 'q' q ω ω norme / : 0.2582 - 0.5164 - 0.7746 - 0.2582 41 mat

q <= that goes in 'quat' converter

6. The rotation 'quat' converter q quat 12 q 3 el (2^* - 2 q 4 el (2^* - 2 q 2 el * q 3 el * 2 q 1 el * q 4 el * - 2 q 1 el * q 3 el * 2 q 2 el * q 4 el * + 2 q 1 el * q 4 el * 2 q 2 el * q 3 el * + 12 q 2 el (2^* - 2 q 4 el (2^* - 2 q 1 el * q 2 el * - 2 q 3 el * q 4 el * + 2 q 1 el * q 3 el * - 2 q 4 el * q 2 el * + 2 q 1 el * q 2 el * 2 q 3 el * q 4 el * + 12 q 2 el (2^* - 2 q 3 el (2^* - 33 mat :

'Unit norme' modulo2 
we feed in 'permute' q 0.258 - 0.516 - 0.775 - 0.258 41 mat

Permute

a q 1 el : b q 2 el : c q 3 el : d q 4 el : 14 mat

Permute  [a,b,c,d]... = 24 ... p a b c d 41 mat a b d c 41 mat a c b d 41 mat a c d b 41 mat a d b c 41 mat a d c b 41 mat b a c d 41 mat b a d c 41 mat b c a d 41 mat b c d a 41 mat b d a c 41 mat b d c a 41 mat c a b d 41 mat c a d b 41 mat c b a d 41 mat c b d a 41 mat c d a b 41 mat c d b a 41 mat d a b c 41 mat d a c b 41 mat d b a c 41 mat d b c a 41 mat d c a b 41 mat d c b a 41 mat 124 mat :

p 0.258 - 0.516 - 0.775 - 0.258 41 mat 0.258 - 0.516 - 0.258 0.775 - 41 mat 0.258 - 0.775 - 0.516 - 0.258 41 mat 0.258 - 0.775 - 0.258 0.516 - 41 mat 0.258 - 0.258 0.516 - 0.775 - 41 mat 0.258 - 0.258 0.775 - 0.516 - 41 mat 16 mat

permuted rotaion 1...24 j 15 :

q p 1 j el :

zoom 7 :

Quaternion rotation => α,β

zoom MAT * q quat * 1 1 sys

q quat ° 42.02 38.2 7.64 7.64 - 19.1 53.48 - 38.2 - 38.2 19.1 33 mat