||

x || y -- a binary operator.

The user may install binary methods for this operator with code such as

              X || Y := (x,y) -> ...

where X is the class of x and Y is the class of y .

s||t -- concatenates strings or nets vertically, yielding a net.f||g -- yields the matrix obtained from matrices f and g by concatenating the columns.

     i1 = R = ZZ/101[a..h]
     
     o1 = R
     
     o1 : PolynomialRing

     i2 = p = matrix {{a,b},{c,d}}
     
     o2 = | a b |
          | c d |
     
                  2       2
     o2 : Matrix R  <--- R

     i3 = q = matrix {{e,f},{g,h}}
     
     o3 = | e f |
          | g h |
     
                  2       2
     o3 : Matrix R  <--- R

     i4 = p || q
     
     o4 = | a b |
          | c d |
          | e f |
          | g h |
     
                  4       2
     o4 : Matrix R  <--- R

If one of the arguments is ring element or an integer, then it will be multiplied by a suitable identity matrix.

     i5 = p || 1
     
     o5 = | a b |
          | c d |
          | 1 0 |
          | 0 1 |
     
                  4       2
     o5 : Matrix R  <--- R