cd6213fe-5a5f-418f-ba03-5df007a3b902 50 3 5 decimal

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Descartes Folium

https://www.mathcurve.com/courbes2d/foliumdedescartes/foliumdedescartes.shtml

a 3 sqrt :

x y f x 3^y 3^+ 3 a * x * y * - :

parametric x 3 a * t * 1 t 3^+ / ≡ y t x * ≡ 21 sys

Area 3 a 2^* 2 / : 4.5

x y asymptote x y + a + :

x y f 0 ≡ y solve maple

x Φ 43 nthroot x 3^- x 3^123 sqrt * - x 3^+ (* sqrt + 3 nthroot (2^x 3 sqrt * 43 nthroot * + (* 2 x 3^- x 3^123 sqrt * - x 3^+ (* sqrt + 3 nthroot * / x 3^- x 3^123 sqrt * - x 3^+ (* sqrt + 3 nthroot (2^x 3 sqrt * 43 nthroot * + i 3 sqrt * x 3^- x 3^123 sqrt * - x 3^+ (* sqrt + 3 nthroot (2^x 3 sqrt * 43 nthroot * - (* - 43 nthroot (2^x 3^- x 3^123 sqrt * - x 3^+ (* sqrt + 3 nthroot * / - x 3^- x 3^123 sqrt * - x 3^+ (* sqrt + 3 nthroot (2^x 3 sqrt * 43 nthroot * + i 3 sqrt * x 3^- x 3^123 sqrt * - x 3^+ (* sqrt + 3 nthroot (2^x 3 sqrt * 43 nthroot * - (* + 43 nthroot (2^x 3^- x 3^123 sqrt * - x 3^+ (* sqrt + 3 nthroot * / - 31 mat :

x Φ 1 el Re x Φ 3 el Re - 0 ≡ x 04 solve 2.741

x y XY x y / - :

Plot companion r 0 x ≤ (x 2.741 ≤ (* : X 2.741 : Y X Φ 1 el : Jct X Y abs + 15 black 15 mat : 41 sys

f asymptote XY 3 1 sys

x Φ 1 el x Φ 1 el Re r / x Φ 3 el Re r / x Φ 2 el Re r / Jct 51 sys

x Φ 1 el x Φ 1 el Re r / x Φ 3 el Re r / x Φ 2 el Re r / Jct 5 1 sys

Mesh U, V  within the bounds L, H L H N xd U 0 : dx H L - N / : i 1 N range U i el L dx i * dx - (+ : for U 41 line :

ε 1012 -^:

N 30 :

u ε 2.741 N xd : v 5.482 - 0 N xd : uu 2.741 0 N xd : vv ε 2.741 N xd : 41 line

Im imaginary ≡

d1 i 1 v rows range d1 i el v i el Φ 1 el eval : for v d1 Re augment 21 line :

d2 i 1 u rows range d2 i el u i el Φ 1 el eval : for u d2 Re augment 21 line :

'i' compatible Im

d3 ii 1 uu rows range d3 ii el uu ii el Φ 3 el eval : for uu d3 Re augment 21 line :

d4 ii 1 vv rows range d4 ii el vv ii el Φ 2 el eval : for vv d4 Re augment 21 line :

'i' NOT compatible Im as it looks, previous compatibility has been consumed NOT recovered.

Alternately . . .

1. collect/global [D]= collapse

2. transit/recover wfile <= rfile

In either preference, stack the

exploded nests ... exploded by

. . . . . . . . . . . . . . . indexing =>

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a stack of 4 nests [d1,d2,d3,d4] D d1 d2 d3 d4 stack :

CWD C:\SmathFile CurrentDirectory :

D CWD V wfile 1

V CWD V rfile :

stack the exploded individual nests N V 1 el V 2 el V 3 el V 4 el stack :

d1 d2 d3 d4 4 1 sys d1 d2 d3 d4 stack N 2 1 sys

OBSERVE: Re(d1) is not needed because d1 is not complex ... it is required to compatiblize the quadruplet

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