# NSolve stops working when solving a system of 54 equations

I am trying to solve a system of 54 second order equations using NSolve. I create a list with the 54 variables and they appear in this way:

{Subscript[a, \[Alpha]][1, 1], Subscript[a, \[Alpha]][2, 0], Subscript[a, \[Alpha]][2, 2], Subscript[a, \[Alpha]][3, 1], Subscript[a, \[Alpha]][3, 3],
...}


I also define the 54 equations in another table in the way

(-Subscript[a, \[Alpha]][1,1]-Subscript[a, \[Alpha]][2,0]+6 Subscript[a, \[Alpha]][2,2]+6 Subscript[a, \[Alpha]][3,1]+3 Subscript[a, \[Alpha]][4,0]-30 Subscript[a, \[Alpha]][4,2]-840 Subscript[a, \[Alpha]][4,4]-45/2 Subscript[a, \[Alpha]][5,1]-210 Subscript[a, \[Alpha]][5,3]+18900 Subscript[a, \[Alpha]][5,5]+6 Subscript[b, \[Alpha]][2,2]+3 Subscript[b, \[Alpha]][3,1]-90 Subscript[b, \[Alpha]][3,3]-60 Subscript[b, \[Alpha]][4,2]+840 Subscript[b, \[Alpha]][4,4]-15 Subscript[b, \[Alpha]][5,1]+840 Subscript[b, \[Alpha]][5,3])^2+(-Subscript[a, \[Beta]][2,0]-6 Subscript[a, \[Beta]][2,2]+3 Subscript[a, \[Beta]][3,1]+90 Subscript[a, \[Beta]][3,3]+3 Subscript[a, \[Beta]][4,0]+30 Subscript[a, \[Beta]][4,2]-840 Subscript[a, \[Beta]][4,4]-15 Subscript[a, \[Beta]][5,1]-840 Subscript[a, \[Beta]][5,3]-Subscript[b, \[Beta]][1,1]+6 Subscript[b, \[Beta]][2,2]+6 Subscript[b, \[Beta]][3,1]-60 Subscript[b, \[Beta]][4,2]-840 Subscript[b, \[Beta]][4,4]-45/2 Subscript[b, \[Beta]][5,1]+210 Subscript[b, \[Beta]][5,3]+18900 Subscript[b, \[Beta]][5,5])^2+(Subscript[a, \[Gamma]][1,0]-3 Subscript[a, \[Gamma]][2,1]-3 Subscript[a, \[Gamma]][3,0]+15 Subscript[a, \[Gamma]][4,1]+210 Subscript[a, \[Gamma]][4,3]+15/2 Subscript[a, \[Gamma]][5,0]-3780 Subscript[a, \[Gamma]][5,4]-3 Subscript[b, \[Gamma]][2,1]+30 Subscript[b, \[Gamma]][3,2]+15 Subscript[b, \[Gamma]][4,1]-210 Subscript[b, \[Gamma]][4,3]-210 Subscript[b, \[Gamma]][5,2])^2==0.0000159221


I checked that both lists have the same length and that the equations and variable are correctly defined. I already tried to solve a simple system using same notation with subscripts and greek letters to check if this function had problems with this notation, and it worked.

The problem is that when I use NSolve for the 54 equations, it is working for some seconds and suddenly stops, but it does not give me any message or error. If I try with Solve insted, it will just work infinitely.

How can I fix this? Is this too complicated to solve in Mathematica?

Thanks.

• TIP: don't use subscripts. – AccidentalFourierTransform Feb 17 '18 at 4:24
• The kernel probably crashed. Maybe due to running out of memory. After it happens, see the menu Help > Why the Beep?... – Michael E2 Feb 17 '18 at 4:33
• I already removed the subscripts and greek letters. Now I just have a1[1,1],... I also checked "Why the Beep?" and this is the message: "The kernel Local has quit (exited) during the course of an evaluation." – Psyphy Feb 17 '18 at 5:27
• Do you need all solutions of these equations? You might use FindRoot (it uses Newton's method) instead in order to obtain only few solutions from initial guesses... – Henrik Schumacher Feb 17 '18 at 9:57
• Try increasing WorkingPrecision in FindRoot; perhaps machine precision is insufficient. You can evaluate the Jacobian yourself to see, check eigen- or singular values, etc....These random guesses are probably the best we can do without working code to examine. – Michael E2 Feb 17 '18 at 19:08