Hi all,
I am trying to solve the following system of equations:
eq1 = 0.8 - 1.8352657742116e-5sqrt(x1(3071.1916x2 + (2.19736842105263e-5 *x3 - 0.378721571752863)(3069.38078875823x1 - 802.539479414006x2 - 802.539479414006x3 + 1187113.71566341))/(2.19736842105263e-5x3 - 0.378721571752863))
eq2 = (-0.00117574932506308x2sqrt(-(0.039945461792316x2 + 0.039945461792316x3 - 71.5306505072653)(3071.1916x2 + 32.9605263157895x3 - 568082.357629294)/(2.19736842105263e-5x3 - 0.378721571752863)) + 1.8352657742116e-5sqrt(x1(3071.1916x2 + (2.19736842105263e-5x3 - 0.378721571752863)(3069.38078875823x1 - 802.539479414006x2 - 802.539479414006x3 + 1187113.71566341))/(2.19736842105263e-5x3 - 0.378721571752863))(x2 + x3))/(x2 + x3)
eq3 = eq3 = (0.007585843252x2(x2 + x3) - 0.00117574932506308x3sqrt(-(0.039945461792316x2 + 0.039945461792316x3 - 71.5306505072653)(3071.1916x2 + 32.9605263157895x3 - 568082.357629294)/(2.19736842105263e-5x3 - 0.378721571752863))(2.19736842105263e-5x3 - 0.378721571752863) + (x2 + x3)(2.19736842105263e-5x3 - 0.378721571752863)(-0.00198227251415259x2 - 0.00198227251415259x3 + 42.4521708776886))/((x2 + x3)(2.19736842105263e-5*x3 - 0.378721571752863))
When I use Symbolic Math Toolbox in Matlab through the following command:
[x1_bar,x2_bar,x3_bar] = solve(eqs,[x1,x2,x3], 'MaxDegree',4);
we get the following results:
x1_bar = ans =
1.0e+04 *
-0.0116 + 0.0000i 0.5338 + 0.0000i -0.0232 + 0.0000i 0.2669 + 0.0000i -0.0047 + 0.0000i 1.3191 + 0.0000i -0.0321 - 0.5445i 0.0007 - 0.0113i -0.0321 + 0.5445i 0.0007 + 0.0113i -0.0012 + 0.0000i 5.1569 + 0.0000i
x2_bar = 1.0e+03 *
1.9653 + 0.0000i 1.9653 + 0.0000i 0.2480 + 0.0000i 0.2480 + 0.0000i -0.6495 + 0.0000i -0.6495 + 0.0000i -0.1794 + 0.2236i -0.1794 + 0.2236i -0.1794 - 0.2236i -0.1794 - 0.2236i -0.0393 + 0.0000i -0.0393 + 0.0000i
x3_bar = 1.0e+04 *
-0.0174 + 0.0000i -0.0174 + 0.0000i 0.6522 + 0.0000i 0.6522 + 0.0000i 4.8817 + 0.0000i 4.8817 + 0.0000i 0.2382 + 2.1159i 0.2382 + 2.1159i 0.2382 - 2.1159i 0.2382 - 2.1159i 1.7273 + 0.0000i 1.7273 + 0.0000i
When I try to solve this problem with Sage using:
S = solve([eq1,eq2,eq3],x1,x2,x3)
I obtain the following results:
[{x1: -321.3551367159828 - 5445.311876550251I, x2: -179.359654094372 - 223.5730259195566I, x3: 2381.999033439763 - 21159.38999334523I}, {x1: 6.685918535164614 - 113.2918302698741I, x2: -179.359654094372 - 223.5730259195566I, x3: 2381.999033439763 - 21159.38999334523I}, {x1: 6.685918535164623 + 113.2918302698741I, x2: -179.359654094372 + 223.5730259195566I, x3: 2381.999033439763 + 21159.38999334523I}, {x1: -321.3551367159836 + 5445.311876550251I, x2: -179.359654094372 + 223.5730259195566I, x3: 2381.999033439763 + 21159.38999334523I}]
I tried also to use the ploynomialRing but it is failing to solve the problem.
Thanks for your help,