Singular

4.13.3 module operations

+

addition (concatenation of the generators and simplification)

*

multiplication with ideal or poly (but not `module` * `module`!)

module_expression [ int_expression , int_expression ]

is a module entry, where the first index indicates the row and the second the column

module_expressions [ int_expression ]

is a vector, where the index indicates the column (generator)

Example:

  ring r=0,(x,y,z),dp;
  module m=[x,y],[0,0,z];
  print(m*(x+y));
==> x2+xy,0,   
==> xy+y2,0,   
==> 0,    xz+yz
  // this is not distributive:
  print(m*x+m*y);
==> x2,0, xy,0,
==> xy,0, y2,0,
==> 0, xz,0, yz