Singular

7.2.3.3 module operations (plural)

+

addition (concatenation of the generators and simplification) Note that "-" implicitely converts a module into a matrix; see below example.

*

right or left multiplication with number, 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 A=0,(x,y,z),Dp;
matrix D[3][3];
D[1,2]=-z;  D[1,3]=y;  D[2,3]=x;  // this algebra is U(so_3)
def B=nc_algebra(1,D);
setring B;
module M = [x,y],[0,0,x*z];
module N = matrix((x+y-z)*M) - matrix(M*(x+y-z)); // no - for type module
print(N);
==> -y-z,0,          
==> -x+z,0,          
==> 0,   -x2-xy-yz-z2