Revision history [back]

Regarding your first question

I get a solution, but i can't extract the single variables of the solution list.

I'm not sure what you mean here. I get:

sage: sols[0]
{C_2_IV: 1/6*(2*(I_R - I_W)*M*a^3 - 2*(I_R*b^3 - I_W*b^3)*M - 3*((I_R - I_W)*M*a^2 - (I_R*b^2 - I_W*b^2)*M)*c)/(I_R*c),
 C_2_III: 1/6*(2*(I_R - I_W)*M*a^3 - 3*(I_R - I_W)*M*a^2*c)/(I_W*c),
 C_2_II: 0,
 C_2_I: 0,
 C_1_IV: -1/6*(2*(I_R - I_W)*M*a^3 + 2*I_R*M*c^3 - 2*(I_R*b^3 - I_W*b^3)*M - 3*((I_R - I_W)*M*a^2 - (I_R*b^2 - I_W*b^2)*M)*c)/(I_R*c^2),
 C_1_III: -1/6*(2*(I_R - I_W)*M*a^3 + 2*I_R*M*c^3 - 6*(I_R*b - I_W*b)*M*c^2 - 2*(I_R*b^3 - I_W*b^3)*M - 3*((I_R - I_W)*M*a^2 - 2*(I_R*b^2 - I_W*b^2)*M)*c)/(I_W*c^2),
 C_1_II: -1/3*((I_R - I_W)*M*a^3 + I_R*M*c^3 + 3*((I_R - I_W)*M*a - (I_R*b - I_W*b)*M)*c^2 - (I_R*b^3 - I_W*b^3)*M - 3*((I_R - I_W)*M*a^2 - (I_R*b^2 - I_W*b^2)*M)*c)/(I_R*c^2),
 C_1_I: -1/3*((I_R - I_W)*M*a^3 + I_R*M*c^3 + 3*((I_R - I_W)*M*a - (I_R*b - I_W*b)*M)*c^2 - (I_R*b^3 - I_W*b^3)*M - 3*((I_R - I_W)*M*a^2 - (I_R*b^2 - I_W*b^2)*M)*c)/(I_R*c^2)}

In this case there is one solution (sols[0]). Since you passed solution_dict=True you get the solutions for each variable as a dict, so the solution for each variable can be extracted like:

sage: sol = sols[0]  # assign the sole solution to its own variable for convenience
sage: sol[C_1_I]

-1/3((I_R - I_W)Ma^3 + I_RMc^3 + 3((I_R - I_W)Ma - (I_Rb - I_Wb)M)c^2 - (I_Rb^3 - I_Wb^3)M - 3((I_R - I_W)Ma^2 - (I_Rb^2 - I_Wb^2)M)c)/(I_R*c^2)

and so on.

The next step would be to make sure that those solutions make sense to you. Check things step be step and make sure that all intermediate results are correct.

Regarding your first question

I get a solution, but i can't extract the single variables of the solution list.

I'm not sure what you mean here. I get:

sage: sols[0]
{C_2_IV: 1/6*(2*(I_R - I_W)*M*a^3 - 2*(I_R*b^3 - I_W*b^3)*M - 3*((I_R - I_W)*M*a^2 - (I_R*b^2 - I_W*b^2)*M)*c)/(I_R*c),
 C_2_III: 1/6*(2*(I_R - I_W)*M*a^3 - 3*(I_R - I_W)*M*a^2*c)/(I_W*c),
 C_2_II: 0,
 C_2_I: 0,
 C_1_IV: -1/6*(2*(I_R - I_W)*M*a^3 + 2*I_R*M*c^3 - 2*(I_R*b^3 - I_W*b^3)*M - 3*((I_R - I_W)*M*a^2 - (I_R*b^2 - I_W*b^2)*M)*c)/(I_R*c^2),
 C_1_III: -1/6*(2*(I_R - I_W)*M*a^3 + 2*I_R*M*c^3 - 6*(I_R*b - I_W*b)*M*c^2 - 2*(I_R*b^3 - I_W*b^3)*M - 3*((I_R - I_W)*M*a^2 - 2*(I_R*b^2 - I_W*b^2)*M)*c)/(I_W*c^2),
 C_1_II: -1/3*((I_R - I_W)*M*a^3 + I_R*M*c^3 + 3*((I_R - I_W)*M*a - (I_R*b - I_W*b)*M)*c^2 - (I_R*b^3 - I_W*b^3)*M - 3*((I_R - I_W)*M*a^2 - (I_R*b^2 - I_W*b^2)*M)*c)/(I_R*c^2),
 C_1_I: -1/3*((I_R - I_W)*M*a^3 + I_R*M*c^3 + 3*((I_R - I_W)*M*a - (I_R*b - I_W*b)*M)*c^2 - (I_R*b^3 - I_W*b^3)*M - 3*((I_R - I_W)*M*a^2 - (I_R*b^2 - I_W*b^2)*M)*c)/(I_R*c^2)}

In this case there is one solution (sols[0]). Since you passed solution_dict=True you get the solutions for each variable as a dict, so the solution for each variable can be extracted like:

sage: sol = sols[0]  # assign the sole solution to its own variable for convenience
sage: sol[C_1_I]
-1/3*((I_R - I_W)*M*a^3 + I_R*M*c^3 + 3*((I_R - I_W)*M*a - (I_R*b - I_W*b)*M)*c^2 - (I_R*b^3 - I_W*b^3)*M - 3*((I_R - I_W)*M*a^2 - (I_R*b^2 - I_W*b^2)*M)*c)/(I_R*c^2)

and so on.

The next step would be to make sure that those solutions make sense to you. Check things step be step and make sure that all intermediate results are correct.

Regarding your first question

I get a solution, but i can't extract the single variables of the solution list.

I'm not sure what you mean here. I get:

sage: sols[0]
{C_2_IV: 1/6*(2*(I_R - I_W)*M*a^3 - 2*(I_R*b^3 - I_W*b^3)*M - 3*((I_R - I_W)*M*a^2 - (I_R*b^2 - I_W*b^2)*M)*c)/(I_R*c),
 C_2_III: 1/6*(2*(I_R - I_W)*M*a^3 - 3*(I_R - I_W)*M*a^2*c)/(I_W*c),
 C_2_II: 0,
 C_2_I: 0,
 C_1_IV: -1/6*(2*(I_R - I_W)*M*a^3 + 2*I_R*M*c^3 - 2*(I_R*b^3 - I_W*b^3)*M - 3*((I_R - I_W)*M*a^2 - (I_R*b^2 - I_W*b^2)*M)*c)/(I_R*c^2),
 C_1_III: -1/6*(2*(I_R - I_W)*M*a^3 + 2*I_R*M*c^3 - 6*(I_R*b - I_W*b)*M*c^2 - 2*(I_R*b^3 - I_W*b^3)*M - 3*((I_R - I_W)*M*a^2 - 2*(I_R*b^2 - I_W*b^2)*M)*c)/(I_W*c^2),
 C_1_II: -1/3*((I_R - I_W)*M*a^3 + I_R*M*c^3 + 3*((I_R - I_W)*M*a - (I_R*b - I_W*b)*M)*c^2 - (I_R*b^3 - I_W*b^3)*M - 3*((I_R - I_W)*M*a^2 - (I_R*b^2 - I_W*b^2)*M)*c)/(I_R*c^2),
 C_1_I: -1/3*((I_R - I_W)*M*a^3 + I_R*M*c^3 + 3*((I_R - I_W)*M*a - (I_R*b - I_W*b)*M)*c^2 - (I_R*b^3 - I_W*b^3)*M - 3*((I_R - I_W)*M*a^2 - (I_R*b^2 - I_W*b^2)*M)*c)/(I_R*c^2)}

In this case there is one solution (sols[0]). Since you passed solution_dict=True you get the solutions for each variable as a dict, so the solution for each variable can be extracted like:

sage: sol = sols[0]  # assign the sole solution to its own variable for convenience
sage: sol[C_1_I]
-1/3*((I_R - I_W)*M*a^3 + I_R*M*c^3 + 3*((I_R - I_W)*M*a - (I_R*b - I_W*b)*M)*c^2 - (I_R*b^3 - I_W*b^3)*M - 3*((I_R - I_W)*M*a^2 - (I_R*b^2 - I_W*b^2)*M)*c)/(I_R*c^2)

and so on.on. For ease of viewing you can also convert it to $ \LaTeX $ :

sage: latex(sol[C_1_I])

$ -\frac{{\left(I_{R} - I_{W}\right)} M a^{3} + I_{R} M c^{3} + 3 \, {\left({\left(I_{R} - I_{W}\right)} M a - {\left(I_{R} b - I_{W} b\right)} M\right)} c^{2} - {\left(I_{R} b^{3} - I_{W} b^{3}\right)} M - 3 \, {\left({\left(I_{R} - I_{W}\right)} M a^{2} - {\left(I_{R} b^{2} - I_{W} b^{2}\right)} M\right)} c}{3 \, I_{R} c^{2}} $

The next step would be to make sure that those solutions make sense to you. Check things step be step and make sure that all intermediate results are correct.