d5667ff5-de1a-45f3-85eb-41b61fc0ffea 10 6 9 decimal

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

chr char ≡

sz size ≡

clr color ≡

vx vy chr sz clr plotG n vx length : plot vx 1 el vy 1 el chr sz clr augment : i 2 n range plot plot vx i el vy i el chr sz clr augment stack : for plot 41 line :

Low High step x fnct inc U Low High step range : i 1 U rows range f i el U i el fnct eval : for U f augment 31 line :

A robust construct of the Scale function M Low High Scale min M Min : max M Max : 12 mat maxmin max min - (1012 -^+ : HighLow High Low - (: i 1 M rows range j 1 M cols range N i j el M i j el min - maxmin / : for for HighLow N * Low + 51 line :

Data 40 0.4 - 80 0.461 - 120 0.483 - 160 1.53 - 200 1.065 240 0.135 280 0.008 - 320 0.039 - 360 0.068 400 0.171 - 102 mat :

X Data 1 col : Y Data 2 col : 21 line

X 01 Scale Y augment 0 0.4 - 0.111111111111111 0.461 - 0.222222222222222 0.483 - 0.333333333333332 1.53 - 0.444444444444443 1.065 0.555555555555554 0.135 0.666666666666665 0.008 - 0.777777777777776 0.039 - 0.888888888888886 0.068 0.999999999999997 0.171 - 102 mat

Data 0 0.4 - 0.111111111111111 0.461 - 0.222222222222222 0.483 - 0.333333333333332 1.53 - 0.444444444444443 1.065 0.555555555555554 0.135 0.666666666666665 0.008 - 0.777777777777776 0.039 - 0.888888888888886 0.068 0.999999999999997 0.171 - 102 mat :

Prepare the Poly model

x φ 1 x x 2^x 3^41 mat :

X Data 1 col : Y Data 2 col : 21 line

j 1 x φ length range i 1 X length range M i j el X i el φ j el : for for Φ M transpose M * : d M transpose Y * : b Φ 1 -^eval d * : 41 line

b 0.4339 - 2.1543 - 9.2933 6.9884 - 41 mat

x fit b x φ * :

<= recast the scalar model

Setup the plot

Poly 01 0.005 x fit inc :

data X Y . 14 red plotG :

3rd order Lagrange PolyFit

Poly data 2 1 sys

Get the roots from the fit

r b polyroots (:

b 0.433917482514064 - 2.15428846158682 - 9.29333391620407 6.98837412595134 - 41 mat

r 0.126198035415732 - 0.533108542985957 0.922917253323868 31 mat

x Lagrange x r 1 el - (x r 2 el - (* x r 3 el - (* :

Render Lagrange/roots ... brute force.
Observe: scale*Lagrange(x)-fit(x) will crash Smath
attempting to plot this Δ(x)...too small numerical. scale r 3 el r 2 el - 2 / r 2 el + fit r 3 el r 2 el - 2 / r 2 el + Lagrange / : 6.9883741259514 -

Alternately: export either b 1 el b 2 el x * + b 3 el x 2^* + b 4 el x 3^* + or scale x r 1 el - (* x r 2 el - (* x r 3 el - (* 31 mat

scale x Lagrange * data Data 3 1 sys

Preference:

Though both forms are identical, the "Lagrange roots" enables further manipulations between the "roots" as "user roots"