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The Smath root(s) solve scanner

The ROBUST root(s) Solve scanner f x0 x1 TOL Solve ρ x f x x0 x1 solve : i 1 ρ rows range a ρ i el 0.1 ρ i el * - : b ρ i el 0.1 ρ i el * + : xn b a + (2 / : ε TOL : n 0 : xn f abs ε > xn f a f * 0 ≤ b xn : a xn : if xn b a + (2 / : n n 1 + : 31 line while 61 line X i el xn : 21 line for X 31 line :

x f x exp x 2^+ 5 x * - :

f 02 Solve #

x f

x f 6 x 3^* 7 x 2^* + 94 x * - 105 + :

x f

Initialise wisely by observing the plot f 5.1 - 2.5 1014 -^Solve 5 - 1.5 2.33333333333334 31 mat

5 - 32 / 73 / 13 mat

x f 1.5 x mwbesselj :

x f

f 0161014 -^Solve 0 4.49340945790908 7.72525183693771 10.9041216594289 14.0661939128315 51 mat

The ROBUST root(s) Intersection Solve scanner f q x0 x1 TOL Solve ρ x f x q - 0 ≡ x x0 x1 solve : i 1 ρ rows range a ρ i el 0.1 ρ i el * - : b ρ i el 0.1 ρ i el * + : xn b a + (2 / : ε TOL : n 0 : xn f xn q - abs ε > xn f xn q - (a f a q - (* 0 ≤ b xn : a xn : if xn b a + (2 / : n n 1 + : 31 line while 61 line X i el xn : 21 line for X 31 line :

x f x 2^:

x q 1.25 :

x f x q 2 1 sys

f q 1.25 - 1.25 1014 -^Solve 1.1180339887499 - 1.1180339887499 21 mat

x f 6 x 3^* 7 x 2^* + 94 x * - 105 + :

x q 128 :

x f x q 2 1 sys

f q 5 - 41012 -^Solve 4.475693 - 0.241243 - 3.55027 31 mat