Solving non linear system of equations

asked 2014-01-04 07:19:38 +0200

Zardoz777
11 ●1 ●1 ●2

updated 2014-01-04 14:06:54 +0200

Shashank

1917 ●30 ●51 ●83

Why this is not working in sage?

f=-V+exp(V)-w-1;
g=0.5*V-w;
sol=solve([f==0,g==0],V,w,solution_dict=True)

It does not return numerical solutions when there are two.

Thanks

answered 2014-01-04 15:14:42 +0200

calc314
4191 ●22 ●48 ●113

The solve command looks for an analytic solution. In this case, the solution will involve the Lambert W function, lambert_w. For some reason, though, Sage is not finding it. (You need to use to_poly_solve=True in the solve command, but Sage is encountering an error.)

To find approximations of the solutions, you can use find_root.

For example,

find_root(-V+exp(V)-0.5*V-1,-1,0.5)

and

find_root(-V+exp(V)-0.5*V-1,0.5,1)

give the two roots.

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Yep. Though in this case it is straightforward to reduce the system into a 1-dimensional equation, it coud be very nice to have `find_root` work with more variables. Also, i do not get an error with `to_poly_solve=True`, just a useless result.

tmonteil ( 2014-01-07 12:44:03 +0200 )edit

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