3489d9de-7380-4dfe-a9d7-152021a51364 6 8 12 decimal

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

Solve implicit algebraic

x y z f 5 x * 6 y z + (* - 8 - 3 x y - (* 2 z * + 6 + x y + z + 2 - 31 mat :

x y z 31 mat x y z f x y z 31 mat roots : 1.818182 2.363636 2.181818 - 31 mat

sanity x y z f 0.000000000000028 0.000000000000031 - 0.00000000000002 - 31 mat

x y z Clear 1

Solve implicit NON-algebraic . . .

A difficult task as many sets of solutions are expected.

In this example, we get [3] sets quite easily. No known

rule(s) are suggested ... trial/error.

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Non-algebraic system f 2 x * y + 2 z 2^* + 5 - 0 ≡ y 3^4 z * + 4 - 0 ≡ x y * z + e z^- 0 ≡ 31 mat :

seed init x 1 ≡ y 1 ≡ z 0.1 ≡ 31 mat :

Accuracy ε 1014 -^:

x y z 31 mat f init ε FindRoot : 1.42246939034512 0.975388528087757 0.768008037465102 31 mat

MCD single set

[set: 1]

sanity 2 x * y + 2 z 2^* + 5 - y 3^4 z * + 4 - x y * z + e z^- 31 mat : 71015 -^* - 11015 -^* - 11014 -^* - 31 mat

x y z Clear 1

Non-algebraic system f 2 x * y + 2 z 2^* + 5 - 0 ≡ y 3^4 z * + 4 - 0 ≡ x y * z + e z^- 0 ≡ 31 mat :

seed init x 1 ≡ y 1 ≡ z 0.1 - ≡ 31 mat :

Accuracy ε 1014 -^:

x y z 31 mat f init ε FindRoot : 1.41584424915365 0.976877013601305 0.777869429079966 31 mat

[set: 2]

sanity 2 x * y + 2 z 2^* + 5 - y 3^4 z * + 4 - x y * z + e z^- 31 mat : 00031 mat

x y z Clear 1

Non-algebraic system f 2 x * y + 2 z 2^* + 5 - 0 ≡ y 3^4 z * + 4 - 0 ≡ x y * z + e z^- 0 ≡ 31 mat :

seed init x 1 ≡ y 1 - ≡ z 1 ≡ 31 mat :

Accuracy ε 1014 -^:

x y z 31 mat f init ε FindRoot : 1.42300421336094 0.974992590477666 0.768057425666393 31 mat

[set: 3]

sanity 2 x * y + 2 z 2^* + 5 - y 3^4 z * + 4 - x y * z + e z^- 31 mat : 00031 mat

γ 1.4 : (Air isentropic ≡ k 0.88128485 : (Pitot constant ≡ p static pressure ≡ qc dynamic pressure ≡ x Pitot dynamic ratio qc/P ≡ x qc p / ≡ (supersonic Pitot ratio ≡ 61 line

Observe the canvas solutions:

as 'x' in Supersonic(x) runs on the plot canvas,

the 'roots' solves and plots each canvas pixel result ...

each result on the basis of 96 ppi [pixel per inch].

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Plot limit x c 10 x ≤ (x 5 ≤ (& cases :

t0 1 time :

x Subsonic 2 γ 1 - / (x 1 + (γ 1 - γ /^1 - (* sqrt 0 x ≤ (x k ≤ (& Supersonic cases : x Supersonic U x 1 + (117 U 2^* / - (2.5^* sqrt / k - 0 ≡ U 1 roots k x ≤ Subsonic cases : 21 line

x Subsonic x Supersonic x c * k 1 + 20 black 1 5 mat 3 1 sys

1 time t0 - 67 s *

supersonic

subsonic

X Y Z q X - Y 1000 / - Z 5000 / - 3625 / + Y 1200 / Y 1000 / + (Z 2000 / - 65 / - Y 2000 / 7 Z * 10000 / Z 4000 / + (- 625 / + 31 mat :

X Y Z 31 mat X Y Z q X Y Z 31 mat roots : 0.45586592 844.69273743 697.20670391 31 mat