Max/Min Golden ratio

e61f65cd-52bb-4d3c-8a57-88f41283e1c1 46 4 5 decimal

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Code adapted from Valery Ochov Mathcad 11 f a b test TOL Extrema a b G 32 / b * 12 / a * - 12 / 5 sqrt * a b - (* + : y1 y2 ≥ (max in range ≡ y1 y2 ≤ (min in range ≡ x1 a b G eval : y1 x1 f eval : x2 b a G eval : y2 x2 f eval : 41 line iter 0 : iter 1000 < a b - abs TOL ≤ break test b x2 : x2 x1 : y2 y1 : x1 a b G eval : y1 x1 f eval : 51 line a x1 : x1 x2 : y1 y2 : x2 b a G eval : y2 x2 f eval : 51 line if iter iter 1 + : 21 line if while a b + 2 / iter 21 mat 71 line :

1. All modules/functions in "Symbolic" optimiz. 2. Once in target: shrink the range 3. respect the search y1≥y2≡"max in range" y1≤y2≡"min in range"

x f x 4^2 x 3^* - 7 x 2^* - 2 - :

X f 1.5 - 1 - y1 y2 ≤ 1012 -^Extrema 1 el f 0.5 - 0.5 y1 y2 ≥ 1012 -^Extrema 1 el f 2.5 3 y1 y2 ≤ 1012 -^Extrema 1 el 31 mat :

X 1.265564 - 2.816018 108 -^* - 2.765564 31 mat

x f X 1 el X 1 el f + 15 red X 2 el X 2 el f + 15 red X 3 el X 3 el f + 15 red 3 5 mat 2 1 sys

x f x 4^2 x 3^* - 7 x 2^* - 2 - : x g x : 21 line

X x f x 3 - 5 solve : 1.9225 - 3.8522 21 mat

C x f x g - 0 ≡ x 3 - 5 solve : 1.837 - 3.8963 21 mat

x f x g X 1 el X 1 el f . 15 red 1 5 mat X 2 el X 2 el f . 15 red 1 5 mat C 1 el C 1 el f o 10 green 1 5 mat C 2 el C 2 el f o 10 green 1 5 mat 6 1 sys

1. roots
2. intersections X C 21 mat 1.9225 - 3.8522 21 mat 1.837 - 3.8963 21 mat 21 mat

b 1.75 :

t Ψ 1 b t 2^- (* t 2^- 2 / exp * :

Morlet wavelet [Mexican hat]

x Ψ

23 sqrt / π 14 / -^* 0.8673

23 sqrt / π 14 / -^* (b t 2^- (* t 2^- 2 / exp *

Max/Min Golden ratio

Code adapted from Valery Ochov Mathcad 11 f a b test TOL Extrema a b G 32 / b * 12 / a * - 12 / 5 sqrt * a b - (* + : y1 y2 ≥ (max in range ≡ y1 y2 ≤ (min in range ≡ x1 a b G eval : y1 x1 f eval : x2 b a G eval : y2 x2 f eval : 41 line iter 0 : iter 1000 < a b - abs TOL ≤ break test b x2 : x2 x1 : y2 y1 : x1 a b G eval : y1 x1 f eval : 51 line a x1 : x1 x2 : y1 y2 : x2 b a G eval : y2 x2 f eval : 51 line if iter iter 1 + : 21 line if while a b + 2 / iter 21 mat 71 line :

1. All modules/functions in "Symbolic" optimiz. 2. Once in target: shrink the range 3. respect the search y1≥y2≡"max in range" y1≤y2≡"min in range"

x f x Ψ :

X f 3 - 1 - y1 y2 ≤ 106 -^Extrema 1 el f 0.125 - 0.125 y1 y2 ≥ 109 -^Extrema 1 el f 13 y1 y2 ≤ 106 -^Extrema 1 el 31 mat :

X 1.936492 - 5.254726 108 -^* - 1.936492 31 mat

iter f 3 - 1 - y1 y2 ≤ 1012 -^Extrema 2 el f 0.5 - 0.5 y1 y2 ≥ 1015 -^Extrema 2 el f 13 y1 y2 ≤ 1012 -^Extrema 2 el 31 mat :

iter 59715931 mat

x f X 1 el X 1 el f + 15 red X 2 el X 2 el f + 15 red X 3 el X 3 el f + 15 red 3 5 mat 2 1 sys

min 'b' = 2 3 sqrt 1.732051