3489d9de-7380-4dfe-a9d7-152021a51364 9 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 - 69 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

Circuit analysis completed by Ber7 [20190204]

knowns V0 1200 : R.1 1000 : R.2 2000 : R.3 3000 : R.4 4000 : R.5 5000 : 61 sys

Voltage drops VA V0 : V.1 VA VB - : V.2 VB VC - : V.3 VB : V.4 VC : V.5 VA VC - : 61 sys

Ohm's law I.1 V.1 R.1 / : I.2 V.2 R.2 / : I.3 V.3 R.3 / : I.4 V.4 R.4 / : I.5 V.5 R.5 / : 51 sys

Coordinates of initial points I0 VB VC f I0 I.1 I.5 + (- 0 ≡ I.1 I.2 I.3 + (- 0 ≡ I.4 I.2 I.5 + (- 0 ≡ 31 mat :

I0 VB VC 31 mat I0 VB VC f I0 VB VC 31 mat roots : 0.4559 844.6927 697.2067 31 mat

VA VB VC V.1 V.2 V.3 V.4 V.5 81 mat 1200 844.6927 697.2067 355.3073 147.486 844.6927 697.2067 502.7933 81 mat

I0 I.1 I.2 I.3 I.4 I.5 61 mat 0.4559 0.3553 0.0737 0.2816 0.1743 0.1006 61 mat

1. label all nodes with letter subscripts. 2. label resistors, their voltage drops and branch current subscript