<p> maple(solve(f(x,y)≡0,x) </p>

47d811f3-9137-47a0-8819-6cf61a3ca466 8 4 5 decimal

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

Solving a system

U y 3 ≡ 3 x * y + 5 ≡ 21 mat :

v x y 21 mat :

U v roots 0.666666666666667 321 mat

A 013122 mat :

v 3521 mat :

A 1 -^v * 0.666666666666667 321 mat

=======================================================

x f x 2^4 - 2 x * 4 x 2^* - 21 mat :

R x f 1 el x f 2 el - x 1 - roots x f 1 el x f 2 el - x 1 roots 21 mat :

x f 1 el x f 2 el R 1 el R 1 el f 1 el + 15 black R 2 el R 2 el f 1 el + 15 black 2 5 mat 3 1 sys

R 0.716515138991168 - 1.11651513899117 21 mat

x f 1 el x f 2 el - 0 ≡ x 1 - 1.5 solve 0.716515179692222 - 1.11651505356483 21 mat

The great Smath/Maple dual solver

x μ colony f colony μ 1 el 11 μ 2 el / 1 - (μ 3 el x μ 4 el - (* - exp * + / + :

# # root

<= a native Maple code, active in Smath but not documented.

1. The general coding to be adapted for each solver

w sol t μ colony f w - t root : colony μ 2 el μ 2 el - 1 + (μ 3 el t μ 4 el - (* - exp * + (* μ 1 el μ 2 el * + w μ 2 el μ 2 el - 1 + (μ 3 el t μ 4 el - (* - exp * + (* - μ 2 el μ 2 el - 1 + (μ 3 el t μ 4 el - (* - exp * + / t root

colony 500 :

simplifiy 1 μ 2 el - (μ 3 el t μ 4 el - (* - exp * μ 2 el + (colony w - (* μ 1 el μ 2 el * + 1 μ 2 el - (μ 3 el t μ 4 el - (* - exp * μ 2 el + /

μ 11000 0.76 1.35 5.037 14 mat transpose :

2. Solving for 'w' [dependent] given 't' independent

w t Sol 1 μ 2 el - (μ 3 el t μ 4 el - (* - exp * μ 2 el + (colony w - (* μ 1 el μ 2 el * + 1 μ 2 el - (μ 3 el t μ 4 el - (* - exp * μ 2 el + / 0 ≡ w 011000 solve :

w 5 Sol 8758.5

Next, we recast the original model from the symbolic 1. above and make 'w=0', that will plot and interpolate the dependent.

t AntColony 1 μ 2 el - (μ 3 el t μ 4 el - (* - exp * μ 2 el + (colony 0 - (* μ 1 el μ 2 el * + 1 μ 2 el - (μ 3 el t μ 4 el - (* - exp * μ 2 el + / :

x λ 10 x ≤ cases :

t 5 :

P t AntColony : 8758.5

8758 t Sol 8758.5

track 0 P t P t 032 mat :

Predictive AntColony Verhulst model fit. What we want from this evolution Colony given 'w' the counted population on the Y ordinate, we want to know the evolution time it toke to populate so many found Y i.e: solve for 't' given 'w'... Sol(w,t)

x μ colony f x λ * track 2 1 sys

w t Sol 1 μ 2 el - (μ 3 el t μ 4 el - (* - exp * μ 2 el + (colony w - (* μ 1 el μ 2 el * + 1 μ 2 el - (μ 3 el t μ 4 el - (* - exp * μ 2 el + / 0 ≡ t 010 solve :

6000 t Sol 4.2

x y f x 3^y 3^- 31 0.4 - (* x * y * - :

y F x y f 0 ≡ x solve maple :

<p> maple(solve(f(x,y)≡0,x) </p>

x F 203 nthroot (2^25 x 3^* 5 sqrt x 3^108 - 125 x 3^* + (* sqrt * + 3 nthroot (2^* 60 x * + 10203 nthroot * 25 x 3^* 5 sqrt x 3^108 - 125 x 3^* + (* sqrt * + 3 nthroot * / 203 nthroot (2^25 x 3^* 5 sqrt x 3^108 - 125 x 3^* + (* sqrt * + 3 nthroot (2^3 x * 203 nthroot * + (203 nthroot (2^* - i 3 sqrt * 203 nthroot (2^25 x 3^* 5 sqrt x 3^108 - 125 x 3^* + (* sqrt * + 3 nthroot (2^* 60 x * - (* + (* 40025 x 3^* 5 sqrt x 3^108 - 125 x 3^* + (* sqrt * + 3 nthroot * / 203 nthroot (2^25 x 3^* 5 sqrt x 3^108 - 125 x 3^* + (* sqrt * + 3 nthroot (2^3 x * 203 nthroot * + (203 nthroot (2^* i 3 sqrt * 203 nthroot (2^25 x 3^* 5 sqrt x 3^108 - 125 x 3^* + (* sqrt * + 3 nthroot (2^* 60 x * - (* + (* 40025 x 3^* 5 sqrt x 3^108 - 125 x 3^* + (* sqrt * + 3 nthroot * / - 31 sys :

x q1 x F 1 el Re eval : x q2 x F 2 el Re eval : x q3 x F 3 el Re eval : 31 sys

u 0.95245 :

X 0.755957587291973 - :

u q2 u q3 - u q3 21 mat 0.000000000000000 0.755957587291973 - 21 mat

ε 1012 -^:

x c2 1 x u ≤ (0 x ≤ (& cases :

x q1 x q2 x c2 * x q3 x c2 * u X + 15 black 1 5 mat 4 1 sys

Uncertified x q3 x ε u int x q2 x ε u int - 0.54

u X 21 mat 0.9524 0.756 - 21 mat