f68d313b-ca98-4f07-8195-dabe189ecfd9 14 4 5 false false 0 0 decimal

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

Iterative solve . . . triplet

x y z f 2 π * x y + 2 z * - (* cos 2 π * y z + 2 x * - (* cos + 2 π * z x + 2 y * - (* cos + :

The solve bloc is generally ≈ 6 decimals
You can initialise a system ... demo

x 0.3 : z 0.1 : 12 mat

The system solves for y from given [x ... z] ▲
This demo produces two sets of solutions
both valid from the sanity check.
Copy/pate 15 decimals ... either y in initial..
Here, braketing is valid wrt [x ... z]

The two sets of solutionsfrom either selecte y 0.1000006 0.0793387 - 0.0999994 - 31 mat 0.4793298 0.4586691 0.2793298 31 mat 12 mat

r x y z f y 0 0.5 solve : 0.120660701354506 0.279339255953666 21 mat

J 2 :

◄  'y' refine manual trial/error initial x x ≡ y r J el : z z ≡ 31 mat :

ε 103 -^:

x z Clear 1

saved in lexicographic order x y z 31 mat x y z f x y z f x y z f 31 mat initial ε FindRoot : 0.4793298 0.4586691 0.2793298 31 mat

sanity implicit f(x,y,z)≡ 0 x y z f 0.0000001

J r Clear 1

x y z Clear 1

u v axes u v / - :

manage shift ellipses ... [0..1] z 0 :

x y Φ 2 π * x y + 2 z * - (* cos 2 π * y z + 2 x * - (* cos + 2 π * z x + 2 y * - (* cos + :

datum 0.145 :

Φ axes datum 3 1 sys

x datum Φ x 1 - 1 solve 0.7825 - 0.5257 - 0.3293 - 0.0725 - 0.2175 0.4743 0.6707 0.9275 81 mat

More plots . . . ▼ governed by z

x y z Clear 1

x y z f 2 π * x y + 2 z * - (* cos 2 π * y z + 2 x * - (* cos + :

[0 ... 1] z 0.5 :

x y f 2 π * x y + 2 z * - (* cos 2 π * y z + 2 x * - (* cos + 2 π * z x + 2 y * - (* cos + :

f 0 0 + 50 red 1 5 mat 2 1 sys

x y z Clear 1

x y z f 2 π * x y + 2 z * - (* cos 2 π * z x + 2 y * - (* cos + :

[0 ... 1] z 0.5 :

x y f 2 π * x y + 2 z * - (* cos 2 π * y z + 2 x * - (* cos + 2 π * z x + 2 y * - (* cos + :

f 0 0 + 50 red 1 5 mat 2 1 sys

x y z u v Clear 1

u v axes u v / - :

manage shift ellipses ... [0..1] z 1 :

x y Φ 2 π * x y + 2 z * - (* cos 2 π * y z + 2 x * - (* cos + 2 π * z x + 2 y * - (* cos + :

Φ axes 2 1 sys

<= Scale a Matrix M Min Max Scale Max Min - (M M min - M max M min - / (* Min + :

Mesh U, V  within the bounds L, H L H N xd N intervals U 0 : dx H L - N / : i 1 N range U i el L dx i * dx - (+ : for U 51 line :

L 0.5 - : H 0.5 : N 96 : 13 mat

U L H N xd :

V U :

x y f x y Φ :

Generate the symmetric square matrix x y f U V Sym r 1 : i 1 U rows range c 1 : j 1 V rows range M r c el U i el V j el f eval : c c 1 + : 21 line for r r 1 + : 31 line for M 31 line :

N x y f U V Sym :

Optimiz: numeric N N 0255 Scale :

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 N 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 N 0 N * N 1 3 mat

Solving numeric a user system ======================

b 1 : c π : 21 line

f a0 0 ≡ a1 c ≡ a1 a2 + a3 + 0 ≡ a1 2 a2 * + 3 a3 * + b ≡ 41 mat :

init a0 1 ≡ a1 1 ≡ a2 1 ≡ a3 1 ≡ 41 mat :

a0 a1 a2 a3 sol f init FindRoot :

solutions in lexicographic order of "init" solutions a0 a1 a2 a3 sol vectorize : 0 3.1416 7.2832 - 4.1416 41 mat

2 c * - b - b c + 21 sys 7.2832 - 4.1416 21 sys

Solving quaternion ======================================

α 0.5 :

β 1.5 :

The Quaternion system f p q + r - 1012 -^≡ p 2^q 2^+ r 2^+ 1 ≡ β p * α r * + 1012 -^≡ 31 mat :

init p 1012 -^≡ q 1012 -^≡ r 1012 -^≡ 31 mat :

Sanity check vs Mathcad 11 f init FindRoot 0.1961 - 0.7845 0.5883 31 mat

p q r 31 mat 0.1961 - 0.7845 0.5883 31 mat

Quaternion p α - 2 α 2^* 2 α * β * + 2 β 2^* + sqrt / α 2 α 2^* 2 α * β * + 2 β 2^* + sqrt / q 12 α 2^* 2 α * β * + 2 β 2^* + sqrt / α β + (* 1 - 2 α 2^* 2 α * β * + 2 β 2^* + sqrt / α β + (* r 12 α 2^* 2 α * β * + 2 β 2^* + sqrt / β * 1 - 2 α 2^* 2 α * β * + 2 β 2^* + sqrt / β * 33 mat :

Next: evaluate numeric

modulo 2 β 2^* 2 β * α * + 2 α 2^* + sqrt :

α 0.5 :

β 1.5 :

Quaternion 2 col 0.1961 - 0.7845 0.5883 31 mat

V α - modulo / α modulo / α β + (modulo / α β + (- modulo / α modulo / α - modulo / 32 mat :

V 0.1961 - 0.1961 0.7845 0.7845 - 0.1961 0.1961 - 32 mat

Next: stack a 'p' value

p 0.6 :

q Quaternion 2 col p stack :

q 0.1961 - 0.7845 0.5883 0.6 41 mat

Nex: the unit vector

q 0.1961 - 0.7845 0.5883 0.6 41 mat :

q q q norme / : 0.1682 - 0.6727 0.5045 0.5145 41 mat

jmG: 20231129