Dropping list elements from nested list after evaluation

Question

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.

Answer 1

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}}

Answer 2

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

{{1, 1, x, 2 x, 3 x}, {1, 1, -x, -2 x, -3 x}}

Answer 3

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}}

Answer 4

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.)