Question

Continuing with my matrix multiplication question, I want to show the following expression in explicit viewable form in mma:

Even if in the case I give a11, …, b11, … explicit numbers, I still want it to be (0&&1)||(1&&1) in unevaluated form. Can anyone please help?

Answer 1

I don’t think this is a really good idea (overloading internal functions and all; and && is And not BitAnd, which you wanted to use in the previous question), but you asked for it and you get it:

CircleTimes[a_?MatrixQ, b_?MatrixQ] := 
 Inner[HoldForm[BitAnd[##]] &, a, b, HoldForm[BitOr[##]] &]

Unprotect[BitAnd];
Unprotect[BitOr];
BitAnd /: Format[BitAnd[a_, b_]] := a && b;
BitOr /: Format[BitOr[a_, b_]] := a || b;
Protect[BitAnd];
Protect[BitOr]

mat1 = Array[Subscript[a, #1, #2] &, {2, 2}];
mat2 = Array[Subscript[b, #1, #2] &, {2, 2}];

The advantage of defining the operation as CircleTimes is that you get the CircleTimes symbol and operator for free.