I am trying to solve equations which looks like this:
$$ T_{ab} - T_{bc} = a_1 T_{ab} + a_2 T_{ac} + a_3 T_{bc}, $$
where $T_{xy}$ are tensors. I want to get the $a_i$'s (in this simple example $a_1=1$, $a_2=0$, $a_3=-1$).
The problem is that the Mathematica solving routines (Solve
, LinearSolve
) divide the equation by $T_{xy}$ to obtain a solution (or solutions), which is (or some of them are), in turn, not a solution (solutions).
What I tried to circumvent this problem:
I know (from the construction of my equation) that all $a_i$'s are element $\{-1,0,1\}$. So I tried to set the domain to integers. But this gives me lots of condidtional solutions (like if Tab=integer, then...
) which I don't want.
Of course I could solve the above example equation by hand, but in the end I will need to solve a few hundred equations of this type with 70 tensors or so.
Thanks in advance for any attempt to help me!
Anton
Mathematica
notation, but something likea_1
,a_2
etc? $\endgroup$Mathematica
code. So if you have different notation in your notebook you can edit your question to make it correct. By the way I didn't vote down your question, I find questions on tensors interesting. $\endgroup$