Ygtjki

I need to create a new list from a nested list but using the evaluation as criteria to drop the elements. For example let's say that that I have the following list:

list1=1,1,-(-1)^3,x,2*x,1,1,(-1)^3,x,2*x,
 1,1,x,2*x,3*x,1,1,-x,-2*x,-3*x

and I need to eliminate the elements of list1 that the absolute value of the third element give $1$, i.d. $-(-1)^3$ and $(-1)^3$, to obtain

 list2=1,1,x,2*x,3*x,1,1,-x,-2*x,-3*x

In this case, list1 was created with the code

For[i = 1, i < 4, i++,
 For[j = 1, j < 4, j++, 
 list1[i, j, p_] = Sort[Eigenvalues[mat[i, j, p]]];
 ] ]

I have been trying to use Select but until now I am not been able to create list2 to plot it with

list2=ParallelTable[Select[Abs[eigval[i, j, p][[3]]], 
 Abs[#] != 1 &] , i, 1, 4, j,1,4]

I am still learning to uses cases in Mathematica so I am not sure how to do it. Do you know if there is wise way to do it? Thanks in advance.

If you prefer using DeleteCases,

list2 = DeleteCases[list1, _?(Abs[#[[3]]] == 1 &)]

1, 1, x, 2 x, 3 x, 1, 1, -x, -2 x, -3 x

Delete[
 list1, 
 Position[Abs[list1[[All, 3]]], 1]
 ]

1, 1, x, 2 x, 3 x, 1, 1, -x, -2 x, -3 x

if you want to use Select, try this

Select[list1,!NumberQ@#[[3]]||Abs[#[[3]]]!=1&] 

1, 1, x, 2 x, 3 x, 1, 1, -x, -2 x, -3 x

This is pretty efficient on unpacked arrays (the Listable attribute assumes list1[[All, 3]] is a flat list, as it is in the OP's example):

Block[signal,
 SetAttributes[signal, Listable];
 signal[1] = 1; signal[_] = 0;
 Pick[list1, signal@Abs[list1[[All, 3]]], 0]
 ]
(* 1, 1, x, 2 x, 3 x, 1, 1, -x, -2 x, -3 x *)

(For packed arrays, one would probably want to use Unitize[x-1] instead of signal.)