25be1940-a872-4dc7-b85e-e82ca925a7f8 104 6 5 decimal

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

Iterate the GivenFind solve bloc

Inspired from Mathcad 8 Pro. It reproduces the solver 1/1. *****

Predefine the solver invariants

a b GivenFind a b FindRoot :

range 100 :

init L 2 ≡ Lc 1 ≡ 21 mat :

A 1011 : V 1500 : 12 mat

i 1 range range idx i el i : d i el 3 i 10 / + : 21 line for

t0 1 time :

Observe:

The solutions appear in the order of "init".

The negative 'Lc' has probably no meaning,

however: does not invalidate the solver.

The meaning of the system is unknown

from the Mathsoft originator ?

Smath 6179 => 2017_06_01

The open style construction is most EDU.

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Solutions [L, Lc] over variable 'd' wrt  'j'
Very robust, the solver supports long range. j system π d j el * L / Lc L - 2 / (2^d j el 2 / (2^+ sqrt * A L / - π d j el 2 / * - ≡ 23 / π L / * d j el 2 / (2^* Lc L - 2 / (* V L / - π d j el 2 / (2^* - ≡ 21 mat :

Generalise an iterative collection of  solutions [L, Lc] j Iterate L Lc Find j system init GivenFind : d sol L Lc Find eval : 21 line above => define the indexed formation d sol 31 line :

Collect the solver j 1 range range : Solved j Iterate vectorize : 21 line

Explode/collect the solved system Plot n 1 range range L n el Solved n el 1 el : Lc n el Solved n el 2 el : 21 line for index [1] Unests solutions d L Lc augment 11 mat 1 el 31 line :

Collect the plot solutions Plot Plot : L Plot 1 col Plot 2 col augment : Lc Plot 1 col Plot 3 col augment : 31 line

Extract indexed sol j 9 : User j Iterate : 21 line

1 time t0 - min 1.8

d j el User 12 mat 3.9 135.37 105.96 21 mat 12 mat

data j d L Lc 14 mat idx d Plot 2 col Plot 3 col augment stack :

_L d j el User 11 el + 15 black 15 mat :_Lc d j el User 21 el + 15 black 15 mat : 21 line

data j d L Lc 1 3.1 200.77 194.67 2 3.2 190.05 179.43 3 3.3 180.2 165.73 4 3.4 171.15 153.33 5 3.5 162.83 142.06 6 3.6 155.15 131.79 7 3.7 148.05 122.42 8 3.8 141.47 113.84 9 3.9 135.37 105.96 104 129.69 98.73 11 4.1 124.39 92.06 124 mat

L Lc 3 200 3 50 - 2 2 mat _L _Lc 5 1 sys

Mutual search from one col to other ... vice-versa

data 1 3.1 200.77 194.67 2 3.2 190.05 179.43 3 3.3 180.2 165.73 4 3.4 171.15 153.33 5 3.5 162.83 142.06 6 3.6 155.15 131.79 7 3.7 148.05 122.42 8 3.8 141.47 113.84 9 3.9 135.37 105.96 104 129.69 98.73 11 4.1 124.39 92.06 114 mat :

Scan down for nearest lower V threshold FindIdx j 1 : V j el abs threshold ≥ j j 1 + : while j 1 - V j el 21 mat 31 line :

V data 3 col :

idx V 145 FindIdx : 7 141.47 21 mat

idx idx 1 el :

other data idx row 14 el : 122.42

Circle/line intersection

D 4 : (Circle ≡

L 0.5 : (Line ≡

Φ vector equalities Φ D x 2^y 2^+ ≡ L x y + ≡ 21 mat :

init x 1 ≡ y 1 ≡ 21 mat :

Collect solutions at kernel level x y sol Φ init FindRoot :

Assign the solutions sol x y sol vectorize : 1.141941 - 1.641941 21 mat

x y 21 mat x y sol vectorize : 1.141941 - 1.641941 21 mat

D x 2 ^ - sqrt D x 2 ^ - sqrt - L x - sol 1 el sol 2 el . 14 black sol 2 el sol 1 el . 14 black 2 5 mat 4 1 sys

D x 2^- sqrt D x 2^- sqrt - L x - sol 1 el sol 2 el . 14 black sol 2 el sol 1 el . 14 black 25 mat 41 sys

jmGiraud: 2015/12/31