Larousir's profile - activity

I just edited my initial question with the raw eqautions.

Waw...Thanks a lot Emmanual for all the efforts you are spending to help on this issue.

I have been trying your proposed solution but I am getting :

J.dimension()
1

I am probably doing something wrong but I will be posting the equations with the original quantities if this can be helpful to debug.

Thanks again for your support.

Thanks Emmanuel and SLelievre for your quick answer.

Really sorry for the formatting issue. I am new to sage and this is the first time I post a question here.

So after taking a quick look on the proposed solution by SLelievre, I guess we need to transform these equations to ploynomials and then use groebner_basis() to solve it rather than roots(). Am I right?

Thanks,

I am trying to solve the following system of equations:

eq1 = 0.8 - 1.8352657742116e-5*sqrt(x1*(3071.1916*x2 + (2.19736842105263e-5 *x3 - 0.378721571752863)*(3069.38078875823*x1 - 802.539479414006*x2 - 802.539479414006*x3 + 1187113.71566341))/(2.19736842105263e-5*x3 - 0.378721571752863))

eq2 = (-0.00117574932506308*x2*sqrt(-(0.039945461792316*x2 + 0.039945461792316*x3 - 71.5306505072653)*(3071.1916*x2 + 32.9605263157895*x3 - 568082.357629294)/(2.19736842105263e-5*x3 - 0.378721571752863)) + 1.8352657742116e-5*sqrt(x1*(3071.1916*x2 + (2.19736842105263e-5*x3 - 0.378721571752863)*(3069.38078875823*x1 - 802.539479414006*x2 - 802.539479414006*x3 + 1187113.71566341))/(2.19736842105263e-5*x3 - 0.378721571752863))*(x2 + x3))/(x2 + x3)

eq3 = (0.007585843252*x2*(x2 + x3) - 0.00117574932506308*x3*sqrt(-(0.039945461792316*x2 + 0.039945461792316*x3 - 71.5306505072653)*(3071.1916*x2 + 32.9605263157895*x3 - 568082.357629294)/(2.19736842105263e-5*x3 - 0.378721571752863))*(2.19736842105263e-5*x3 - 0.378721571752863) + (x2 + x3)*(2.19736842105263e-5*x3 - 0.378721571752863)*(-0.00198227251415259*x2 - 0.00198227251415259*x3 + 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 - 5445.311876550251*I,
  x2: -179.359654094372 - 223.5730259195566*I,
  x3: 2381.999033439763 - 21159.38999334523*I},
 {x1: 6.685918535164614 - 113.2918302698741*I,
  x2: -179.359654094372 - 223.5730259195566*I,
  x3: 2381.999033439763 - 21159.38999334523*I},
 {x1: 6.685918535164623 + 113.2918302698741*I,
  x2: -179.359654094372 + 223.5730259195566*I,
  x3: 2381.999033439763 + 21159.38999334523*I},
 {x1: -321.3551367159836 + 5445.311876550251*I,
  x2: -179.359654094372 + 223.5730259195566*I,
  x3: 2381.999033439763 + 21159.38999334523*I}]

I tried also to use the PolynomialRing but it is failing to solve the problem.

EDIT : Here are the raw equations with the original quantities:

eq1 =w_G_a_in - K_a*sqrt((x1*(R*T_a + g*L_a*M_G_a)*((g*L_a*x1)/V_a - 
    (g*L_r*(x2 + x3 - L_bh*S_bh*rho_L))/V_r - F_riser + (R*T_a*x1)/(V_a*M_G_a)
    + (R*T_r*rho_L*x2)/(M_G_r_t*(x3 - V_r*rho_L + L_bh*S_bh*rho_L))))/(R*T_a*V_a))



eq2 =K_a*sqrt((M_G_a*((g*L_a*x1)/V_a + (R*T_a*x1)/(V_a*M_G_a))*((g*L_a*x1)/
    V_a - (g*L_r*(x2 + x3 - L_bh*S_bh*rho_L))/V_r - F_riser + (R*T_a*x1)/(V_a*M_G_a)
    + (R*T_r*x2)/(M_G_r_t*(L_bh*S_bh - V_r + x3/rho_L))))/(R*T_a))-(GOR*PI*(2*F_riser - P_r + g*L_bh*rho_L + (g*L_r*(x2 + x3 - L_bh*S_bh*rho_L))/V_r 
 - (R*T_r*x2)/(M_G_r_t*(L_bh*S_bh - V_r + x3/rho_L))))/(GOR + 1) - (K_r*u1*x2*
 sqrt(-((P0 + (R*T_r*x2)/(M_G_r_t*(L_bh*S_bh - V_r + x3/rho_L)))*(x2 + x3 - L_bh*S_bh*rho_L))/V_r))/(x2 + x3)



eq3 =PI*(GOR/(GOR + 1) - 1)*(2*F_riser - P_r + g*L_bh*rho_L + (g*L_r*(x2 + x3
     - L_bh*S_bh*rho_L))/V_r - (R*T_r*x2)/(M_G_r_t*(L_bh*S_bh - V_r + x3/rho_L)))
- (K_r*u1*x3*sqrt(-((P0 + (R*T_r*x2)/(M_G_r_t*(L_bh*S_bh - V_r + x3/rho_L)))*(x2 + x3 - L_bh*S_bh*rho_L))/V_r))/(x2 + x3)