Mathematica Mathematica: Solve System of Eqs & Create Table

[ilvreth]

Hi to all!

Again I have a question in mathematica.

Lets us define a system of equations e.q.

eqs1 =-0.17544 Csc[\[Theta]]^2 + Sin[2 \[Phi]] == 0 && 
0.001447 - 0.0864 Cos[\[Theta]] + 0.0288 Cos[\[Theta]]^3 == 0;

and we want to find the solution by optimization with

Reduce[{eqs1 && 0 <= \[Phi] <= 2 \[Pi] && 
   0 <= \[Theta] <= \[Pi]}, {\[Phi], \[Theta]}, Reals]

The result we obtain for example is something like here

(\[Phi] == 0.0882006 && \[Theta] == 1.55405) || (\[Phi] == 
    1.4826 && \[Theta] == 1.55405) || (\[Phi] == 
    3.22979 && \[Theta] == 1.55405) || (\[Phi] == 
    4.62419 && \[Theta] == 1.55405)

We obtain 4 pairs of solutions.
The question is, how we can store these pairs of solutions Phi and Theta into a table as elements so we can easily use them later for instance we want to store the pair solution

\[Phi]=0.0882006 , \[Theta] = 1.55405
as matrix elements like this A[1,1]=0.0882006, A[1,2]= 1.55405.

How this can be done automatically without repeated copy-paste with the mouse for houres?

 

[DrClaude]

One possibility is

sol = Solve[(\[Phi] == 0.0882013 && \[Theta] == 1.55405) || (\[Phi] == 
      1.48259 && \[Theta] == 1.55405) || (\[Phi] == 
      3.22979 && \[Theta] == 1.55405) || (\[Phi] == 
      4.62419 && \[Theta] == 1.55405), {\[Theta], \[Phi]}]

followed by

A = {\[Phi], \[Theta]} /. sol

which results in

{{0.0882013, 1.55405}, {1.48259, 1.55405}, {3.22979, 
  1.55405}, {4.62419, 1.55405}}

 

[ilvreth]

Oh, it was so easy finally..
Thank you!