special boolean operator

Question

I am familiar with some boolean operators. I want to access an operator that does a procedure same as below one. But for simplicity, we can say in the first step we ignore i and jth part of lists in order to use above operators. But for i and jth part we just add them to each other. I mean

IF except i and j according elements of two lists are different, the output has to be zero. For example in {0,1,0,0,1},{1,1,0,0,1} the first element of the first list is 0 but the first element of the second list is 1. The result has to be zero. but if there is not a such situation, I mean even if i and j be different but other elements are accordingly (one by one) equal, the result has to be in a such way that i and jth parts added accordingly but instead of other element must be put zero.

Assume: i=2;j=5;
Oerator[{0,1,0,0,1},{0,1,0,0,1}]={0,2,0,0,2};
Oerator[{1,1,0,0,1},{1,1,0,0,1}]={0,2,0,0,2};
Oerator[{0,1,0,0,1},{1,1,0,0,1}]=0;
Oerator[{0,1,0,0,1},{0,0,0,0,1}]={0,1,0,0,2};
Oerator[{0,1,0,0,1},{0,1,0,0,0}]={0,2,0,0,1};
Oerator[{0,1,0,1,1},{0,0,0,0,1}]=0;
Oerator[{0,1,0,1,1},{0,0,0,1,1}]={0,1,0,0,2};

Answer 1

Now that you have clarified what you want, I'll post my (slightly modified) attempt from the comments as an answer:

Operator[i__][o__] :=
 If[
  Equal @@ {o}[[All, Complement[Range@Length@First@{o}, {i}]]],
  Normal[
   Total@{o} SparseArray@Thread[{i} -> 1]
  ],
  0
 ]

It is used as

Operator[2,5][{0,1,0,0,1},{0,1,0,0,1}]
Operator[2,5,6][{0,1,0,1,0,1},{0,1,0,0,1,1}]
MyOp = Operator[2,5]
MyOp[{0,1,0,0,1},{0,1,0,0,1}]

(works with an arbitrary amount of operands and indexes)

How it works:

• Complement[Range@Length@First@{l}, {i}] gets all indexes except the specified ones
• These indexes are then extracted from All operands {o}
• If the resulting lists are Equal:
  • Take the Total of all operands (element wise)
  • Multiply the result (element wise), with array where only indexes {i} are 1, the rest is 0
• Otherwise, return 0